OGIC    AND 
ARGUMENT 


THE  LIBRARY 

OF 

THE  UNIVERSITY 

OF  CALIFORNIA 

LOS  ANGELES 

PROFESSOR  JOHN  ELOF  BOODIN 

MEMORIAL  PHILOSOPHY 

COLLECTION 


LOGIC    AND   ARGUMENT 


LOGIC   AND 
ARGUMENT 


BY 

JAMES   H.   HYSLOP 


CHARLES   SCRIBNER'S   SONS 
NEW   YORK    1899 


COPYRIGHT,  1899,  BY 
CHARLES  SCRIBNER'S  SONS 


TROW  DIRECTORY 
NEW  YORK 


PREFACE 

THIS  work  has  been  written  to  supply  a  double 
want,  namely,  the  combination  of  a  purely  ele- 
mentary logic  with  the  art  of  argumentative  dis- 
course. Nor  has  this  last  feature  of  the  subject 
been  added  out  of  deference  to  a  revival  of  an  in- 
tellectual interest  in  collegiate  debate,  but  it  has 
been  suggested  both  by  the  practical  value  of 
logic  as  mental  discipline  and  its  close  connection 
with  the  proper  and  orderly  discussion  of  all  sub- 
jects in  which  educated  men  are  expected  to  en- 
gage. Logic  as  a  practical  art  may  be  made  quite 
free  from  discussion  of  the  theory  of  knowledge ; 
and  thus  free  from  philosophic  problems,  may  be 
made  most  serviceable  in  the  field  of  clear  and 
systematic  thinking  wherever  a  man  is  called  upon 
to  form  and  express  his  opinions.  The  author  has 
long  felt  that  formal  and  applied  logic  of  the  ele- 
mentary kind  can  be  taught  as  well  in  the  earlier  as 
in  the  later  part  of  a  collegiate  course,  so  that  the 
student  can  receive  the  benefit  of  it  throughout 
his  whole  academic  career.  It  is  especially  a  sub- 
ject which  ought  to  follow  closely  upon  mathe- 
matics. The  value  of  this  latter  science  lies  in 
the  habit  of  reasoning  which  it  fosters,  but  it 
labors  under  one  grave  fault,  if  it  is  not  supple- 

1C9&595 


vi  PREFACE 

mented  by  a  knowledge  of  practical  logic  on  other 
data,  and  this  is  the  encouragement  which  it  may 
unconsciously  offer  to  over-confidence  in  the 
legitimacy  of  our  reasoning  in  subjects  where  our 
propositions  do  not  resemble  those  in  mathema- 
tics. Mathematics  is  the  most  important  science 
in  which  to  begin  our  discipline  in  reasoning, 
because  we  are  not  complicated  with  all  those 
modifications  of  meaning  which  the  subjects  of 
distribution  and  equivocation  introduce  into  the 
process  in  other  sciences.  But  it  ought  to  be  fol- 
lowed closely  by  logic  in  a  long  and  careful  appli- 
cation to  practical  examples  that  may  contribute 
to  general  knowledge  while  they  also  effect  men- 
tal discipline. 

Fora  somewhat  similar  reason  I  have  connected 
it  with  one  department  of  rhetoric,  but  only  that 
which  is  concerned  with  the  treatment  of  argu- 
ments. But  I  have  not  more  than  merely  outlined 
this  aspect  of  the  subject,  leaving  to  the  instructor 
the  development  both  of  detailed  rules  and  of 
practical  work  in  themes.  The  outline  and  dis- 
cussion of  any  thesis  often  depends  upon  a  variety 
of  circumstances  for  which  only  the  most  general 
rules  can  be  given,  and  hence  I  have  endeavored 
only  to  assist  the  teacher  in  saving  time  by  giv- 
ing the  student  the  general  principles  in  order  to 
limit  the  amount  of  lecturing  and  dictation.  The 
practical  exercises  will  afford  all  the  opportunity 
necessary  for  the  special  elucidation  of  principles. 

The  work  has  also  been  written  so  that  the  part 
devoted  to  rhetoric  can  easily  be  omitted  and  the 


PREFACE  vii 

remainder  used  for  purely  elementary  logic.  The 
treatment  of  induction  has  been  made  very  brief, 
as  not  being  adapted  to  as  easy  mastery  as  de- 
ductive logic.  But  I  have  carefully  outlined  the 
subject  of  fallacies  and  methods  of  argumenta- 
tion. It  is  hoped  that  the  work  may  encourage 
an  earlier  study  of  logic  than  prevails  in  many  in- 
stitutions. 

JAMES  H.  HYSLOP. 

COLUMBIA  UNIVERSITY, 
May  22,  1899. 


CONTENTS 

CHAPTER   I. 
INTRODUCTION. 

I.  NATURE  OF  THE  SUBJECT  :  Definition  of  Logic — Defini- 
tion of  Rhetoric.  II.  SCOPE  OF  LOGIC  :  Meaning  of  Law — 
Meaning  of  Thought  —  Prelogical  Processes  —  The  Logical 
Processes.  III.  SCOPE  OF  DISCOURSE  :  Divisions  of  Idea 
Expression — The  Functions  of  Discourse — Explanation — Con- 
firmation. IV.  SUMMARY,  ....  Pages  1-17 

CHAPTER  II. 
CLASSIFICATION  OF  TERMS  OR   CONCEPTS. 

I.  DEFINITION  OF  TERMS.  II.  DIVISION  OF  TERMS: 
Categorematic  and  Syncategorematic  Terms  —  Singular  and 
General  Terms — Collective  and  Distributive  Terms — Concrete 
and  Abstract  Terms — Positive  and  Negative  Terms — Absolute 
and  Relative  Terms,  .....  Pages  18-30 

CHAPTER   III. 
THE   CONTENT  OF   TERMS. 

I.  INTRODUCTION.  II.  EXPLANATION  OF  THE  PREDI 
CABLES  :  Extension  —  Intension.  III.  ANALYSIS  OF  CON- 
CEPTS: Definition — Division — Partition,  .  Pages  31-52 


X  CONTENTS 

CHAPTER   IV. 
EXPLANATORY   DISCOURSE. 

I.  INTRODUCTION.  II.  ANALYSIS  OF  THEMES:  Applica- 
tion and  Use  of  Definition — The  Application  and  Use  of  Di- 
vision— The  Application  and  Use  of  Partition  —  Methods  of 
Applying  Analysis.  III.  SYNTHESIS  OR  COMPOSITION  :  Laws 
of  Composition  or  Synthesis  —  Forms  of  Composition.  IV. 
CONCLUSION Pages  53-71 


CHAPTER  V. 
PROPOSITIONS. 

I.  DEFINITION.  II.  DIVISIONS:  Univocal  Propositions — 
Equivocal  Propositions.  III.  DISTRIBUTION  OF  TERMS, 

Pages  72-92 

CHAPTER   VI. 
OPPOSITION. 

I.  MEANING  OF  OPPOSITION.  II.  LAWS  OF  OPPOSITION. 
III.  SPECIAL  CASES.  IV.  PRACTICAL  APPLICATION  OF  OP- 
POSITION, .  .  .  .  .  .  Pages  93-102 


CHAPTER   VII. 
IMMEDIATE   INFERENCE. 

I.  DEFINITION.  II.  DIVISIONS:  Conversion — Obversion, 
Contraversion  or  Contraposition — Inversion — Contribution — 
Antithesis,  ......  Pages  103-117 


CONTENTS  XI 

CHAPTER   VIII. 
MEDIATE    REASONING. 

I.  DEFINITION.  II.  DIVISIONS.  III.  ELEMENTS  OF  THE 
SYLLOGISM.  IV.  RULES  FOR  THE  SYLLOGISM  :  Rules  Affect- 
ing the  Subject-Matter  of  the  Syllogism  —  Rules  Affecting 
the  Quantity  and  Quality  of  Propositions.  V.  MOODS  OF  THE 
SYLLOGISM.  VI.  FIGURES  OF  THE  SYLLOGISM.  VII.  REDUC- 
TION OF  MOODS  AND  FIGURES.  VIII.  PRACTICAL  IMPOR- 
TANCE OF  THE  FIGURES,  .  .  .  Pages  118-130 

CHAPTER   IX. 

SIMPLE   AND    COMPLEX    FORMS    OF    CATEGORI- 
CAL  REASONING. 

I.  CLASSIFICATION  OF  FORMS.  II.  EXPOSITION  :  Prosyl- 
logism  and  Episyllogism  —  Enthymeme  —  Epicheirema  — 
Sorites, Pages  131-137 

CHAPTER    X. 
HYPOTHETICAL   REASONING. 

I.  NATURE  AND  DIVISIONS.  II.  SIMPLE  HYPOTHETICAL 
SYLLOGISMS.  III.  DILEMMATIC  REASONING.  IV.  REDUC- 
TION OF  HYPOTHETICAL  TO  CATEGORICAL  REASONING, 

Pages  138-148 

CHAPTER   XI. 
DISJUNCTIVE   REASONING. 

I.  NATURE  OF  DISJUNCTIVE  REASONING.  II.  FORMS  OF 
DISJUNCTIVE  REASONING.  III.  REDUCTION  OF  DISJUNC- 
TIVE SYLLOGISMS, Pages  149-154 


XJi  CONTENTS 

CHAPTER   XII. 
FALLACIES. 

I.  DEFINITION  AND  DIVISIONS.  II.  FORMAL  FALLACIES  : 
Illicit  Process  of  the  Middle  Term — Illicit  Process  of  the  Ma- 
jor Term — Illicit  Process  of  the  Minor  Term — Illicit  Process 
with  Negative  Premises — Illicit  Process  with  Mixed  Premises 
and  Conclusions.  III.  MATERIAL  FALLACIES  :  Fallacies  of 
Equivocation — Fallacies  of  Presumption.  IV.  GENERAL  OB- 
SERVATIONS,   Pages  155-184 

CHAPTER    XIII. 
INDUCTIVE   REASONING. 

I.  GENERAL  NATURE  OF  INDUCTIVE  REASONING  :  Perfect 
Induction — Imperfect  Induction — Definition  of  Inductive  Rea- 
soning. II.  FORMAL  PROCESS  IN  INDUCTION.  III.  IN- 
DUCTIVE FALLACIES,  ....  Pages  185-191 

CHAPTER   XIV. 
PROOF  AND   ARGUMENTATION. 

I.  INTRODUCTION:  Nature  of  Proof— Kinds  of  Proof.  II. 
PROCESS  OF  PROOF  OR  ARGUMENT:  Definition — Analysis- 
Probation.  III.  CLASSIFICATION  AND  ARRANGEMENT  OF 
ARGUMENTS:  Forms  of  Argument— Arrangement  of  Argu- 
ments, .......  Pages  192-214 

QUESTIONS  AND   EXAMPLES,         .         .        Page  215 


LOGIC   AND    ARGUMENT 


LOGIC  AND  ARGUMENT 


CHAPTER  I 
INTRODUCTION 

I.  NATURE  OF  THE  SUBJECT.— Two  sci- 
ences or  arts,  as  the  case  may  be,  are  represented 
in  the  title  to  this  book.  They  are  Logic  and 
Rhetoric.  But  the  whole  province  of  both  of 
them  will  not  be  comprised  in  this  one  treatise. 
Only  those  portions  of  their  territory  which  are 
closely  allied  will  be  comprehended  in  the  plan 
before  us,  which  will  be  to  combine  the  principles 
of  correct  reasoning  with  those  of  systematic  and 
orderly  discourse.  The  more  scientific  portion  of 
Logic  and  the  more  literary  aspect  of  Rhetoric 
will  be  omitted,  while  we  unite  the  practical  func- 
tions of  the  former  with  the  systematic  principles 
of  the  latter.  Discourse  will  thus  get  its  treat- 
ment from  a  point  of  view  which  involves  both 
a  method  of  logical  reasoning  and  a  systematic 
form  of  constructing  the  material  of  thought, 
while  the  scientific  object  of  the  one  and  the 
aesthetic  object  of  the  other  give  way  to  the  one 
purpose  of  teaching  the  student  to  logically  sys- 


2  LOGIC   AND    ARGUMENT 

tematize  the  knowledge  which  he  acquires.  In  or- 
der to  show  the  relation  of  the  two  subjects  to 
each  other  and  the  mode  of  their  present  com- 
binations,  a  careful  definition  and  explanation  of 
their  contents  is  necessary. 

ist.  Definition  of  Logic. — Logic  may  be  treated 
either  as  a  science  or  an  art,  or  both.  As  a  science 
it  seeks  to  determine  what  are  called  the  laws  of 
thought,  which  is  represented  in  the  three  processes 
of  conception,  judgment,  and  reasoning.  As  an  art 
it  applies  these  laws  or  rules  to  every-day  thought. 
Thus  a  science  teaches  us  to  know,  and  art  to  do. 
But  the  distinction  does  not  require  to  be  urged 
for  present  purposes.  The  object  here  is  to  se- 
lect just  those  parts  of  both  aspects  that  are  suit- 
able to  systematic  and  logical  discourse,  as  dis- 
tinct from  mere  description,  on  the  one  hand,  and 
pure  science  on  the  other.  Consequently  we  may 
speak  and  think  of  logic  from  its  practical  side, 
or  so  much  of  it  as  pertains  to  orderly  methods  of 
statement  and  argument.  Logic  for  this  purpose 
will  consist  of  the  rules  that  regulate  correct 
thinking  and  systematic  presentation  of  ideas, 
more  especially  in  the  form  of  argument.  As  a 
whole  it  has  two  objects  to  fulfil  :  (i)  To  deter- 
mine the  general  laws  of  thought  which  are  called 
the  formal  principles  of  thinking,  and  (2)  To  ex- 
plain the  conditions  under  which  these  laws  are  to 
be  applied  and  to  be  modified  by  the  irregularities 
of  language  and  common  speech.  The  first  object 
considers  logic  as  a  pure  science,  the  second  as  an 
applied  science  or  art.  Only  the  latter  aspect  will 
enter  into  the  purpose  of  the  present  treatise. 


INTRODUCTION  3 

2d.  Definition  of  Rhetoric — Rhetoric  may  also 
be  considered  as  either  or  both  a  science  and  an 
art.  Like  logic,  it  has  to  do  with  the  form  of  dis- 
course or  the  presentation  of  ideas.  But  it  in- 
cludes some  things  not  considered  by  logic  and 
omits  some  things  included  in  logic.  In  both 
cases,  however,  it  has  a  different  object.  It  is  not 
directly  concerned  with  the  rules  of  reasoning, 
nor  with  the  truth  of  propositions  and  discourse, 
but  with  their  form  of  expression.  It  is,  there- 
fore, the  science  and  art  of  the  aesthetic  and  correct 
expression  of  ideas.  Consequently  it  will  include 
descriptive  and  narrative  methods  not  found  in 
logic  while  it  insists  upon  beauty  of  form,  and 
omits  investigation  of  the  laws  of  reasoning,  while 
it  insists  upon  orderly  construction  of  ideas  in  ac- 
cordance with  the  principles  of  logical  discourse. 
There  are  also  then  two  aspects  to  rhetoric  :  (i) 
Beauty  of  form  and  expression,  and  (2)  Systematic 
and  orderly  expression  with  a  view  to  efficiency  in 
imparting  ideas.  The  former  is  the  literary  and 
aesthetic  aspect,  and  the  latter  the  discursive  and 
persuasive  function  of  the  subject.  But  it  is  only 
the  latter  aspect  that  will  enter  into  the  present 
book,  and  only  so  much  of  it  as  directly  relates  to 
logical  method. 

II.  SCOPE  OF  LOGIC.— In  common  usage 
logic  is  understood  to  treat  of  reasoning  alone  and 
its  laws.  But  it  has  a  wider  field.  The  laws  of 
thought  apply  to  much  more  than  reasoning,  but 
only  because  "  thought "  is  more  than  inference. 
It  treats  of  all  the  complex  processes  of  knowledge 
as  distinct  from  the  simple  and  elementary  func- 


4  LOGIC    AND    ARGUMENT 

tions  of  the  mind,  and  in  addition  lays  special  em- 
phasis upon  the  rules  which  determine  the  dis- 
tinction between  true  and  false  thinking  rather 
than  upon  the  causes  of  mental  phenomena.  It 
omits  the  consideration  of  all  elementary  data  of 
knowledge,  such  as  sensation,  perception,  associa- 
tion, memory,  and  the  mental  states  connected 
with  art  and  ethics,  the  emotions,  desires,  and  voli- 
tions, and  confines  attention  to  the  three  functions 
which  constitute  "thought;"  namely,  (i)  The 
laws  of  Conception  ;  (2)  The  laws  of  Judgment, 
and  (3)  The  laws  of  Inference.  Each  of  these 
will  come  up  for  study  in  the  proper  place.  At 
present  we  must  ascertain  more  definitely  what  is 
meant  by  "  laws  of  thought." 

ist.  Meaning  of  Law. — The  term  "law"  has 
three  meanings,  one  in  politics  and  ethics,  and 
two  in  science.  They  are  (i)  A  command  or  pro- 
hibition, an  injunction  either  by  government  or  by 
conscience  to  do  or  not  to  do  ;  (2)  The  uniformity 
of  events,  or  the  fixed  regularity  with  which  events 
occur  under  conditions  determining  them  ;  and 
(3)  A  rule  which  serves  as  a  criterion  of  what  is 
true  or  false.  This  is  sometimes  called  a  princi- 
ple, and  is  distinguished  from  a  cause  in  the  or- 
dinary sense  of  that  term.  With  the  first  of 
these  senses  logic  has  nothing  to  do.  It  concerns 
only  the  other  two  with  special  reference  to  the 
third  inasmuch  as  it  is  mainly  occupied  with  the 
means  of  distinguishing  between  truth  and  error, 
so  far  as  conception,  judgment,  and  reasoning  are 
connected  with  them.  In  science  "law"  is  either 
a  name  for  mere  uniformity  of  events  beyond  our 


INTRODUCTION  5 

ability  to  modify  them,  or  it  is  a  name  for  a  prin- 
ciple or  rule  of  our  own  action  in  which  we  en- 
deavor to  shape  our  thinking,  feeling,  and  willing 
to  the  conditions  of  things  outside  of  us  as  well 
as  in  the  mind.  Logic  thus  tries  to  find  the  uni- 
formities of  mental  operations  and  to  put  us  in 
the  way  of  conforming  to  them  correctly,  or  ap- 
plying them  so  that  illusion  and  error  in  knowl- 
edge and  belief  may  not  occur.  In  the  present 
treatise,  however,  we  shall  not  occupy  ourselves 
with  the  determination  of  these  laws  as  mere  uni- 
formities of  events,  but  as  rules  to  be  kept  in 
mind  when  engaged  in  discourse  or  argument, 
and  hence  as  helps  to  systematic  and  clear  think- 
ing. For  this  purpose  we  do  not  require  to  study 
the  most  general  "  laws "  of  thought,  but  only 
those  minor  and  subordinate  rules  connected  with 
the  use  of  conceptions,  judgments,  and  reasoning, 
and  which  may  be  understood  without  a  profound 
acquaintance  with  our  subject. 

2d.  Meaning  of  Thought. — This  term  has  more 
than  one  meaning,  only  one  of  which  is  of  in- 
terest in  logical  discourse.  We  may  enumerate 
four  of  its  meanings  :  (i)  Consciousness,  (2)  Med- 
itation, (3)  Comparison,  (4)  Reasoning.  The  first 
means  merely  "  to  have  in  mind,"  and  involves  no 
special  laws  of  importance  in  logic.  The  second 
denotes  reflection,  or  holding  the  attention  upon 
some  object  of  consciousness.  The  third  and 
fourth  usually  imply  this  reflection,  but  denote 
more  at  the  same  time.  They  do  not,  however, 
represent  the  most  comprehensive  idea  of  the 
term  which  combines  them  and  which  may  be 


6  LOGIC   AND    ARGUMENT 

called  synthesis.  Thought  or  synthesis,  as  a  log- 
ical process,  may  be  defined  as  the  mental  act 
which  compares,  combines,  and  unifies  experience 
so  as  to  produce  clear  knowledge.  This  idea  in- 
cludes more  than  mere  inference,  and  so  compre- 
hends all  the  processes  that  are  connected  with 
the  formation  of  complex  as  distinct  from  simple 
ideas.  Consequently  in  logic  it  is  a  term  that 
comprehends  all  the  mental  actions  connected 
with  conception,  judgment,  and  reasoning.  These 
are  occupied  with  complex  ideas.  The  earlier  and 
prelogical  processes  are  connected  with  simple 
ideas,  as  they  are  often  called  :  the  mental  states 
which  do  not  compare,  discriminate,  or  unite  ex- 
periences to  form  thought  wholes.  Both  classes  of 
mental  action  may  come  in  for  brief  consideration. 

1.  Prelogical  Processes. — These  are  :    (i)  Sen- 
sation, the  definite  states  of  consciousness  effected 
by  the  mind's  reaction  upon  stimulus  from  the  ex- 
ternal world  ;  (2)  Apprehension  or  Perception,  the 
act  of  being  aware  of  a  fact  that  it  is,  not  neces- 
sarily what  it  is  ;  (3)  Memory,  involving  the  reten- 
tion, reproduction,  or  association  and  the  recogni- 
tion of  past  experiences.    These  are  all  elementary 
acts   of  the   mind,   not   involving  comparison   or 
unification  of  any  kind.     They  represent   simple 
states  of  consciousness  and  simple  subject-matter. 
They  are  the  material  or  the  occasion  for  calling 
into  action  the  higher  exercise  of  the  understand- 
ing, but  they  are  not  themselves  logical  processes 
in  the  technical  sense  of  the  term. 

2.  The  Logical  Processes — These  are  one  and 
all  acts  of  the  mind  which  conceive  a  connection 


INTRODUCTION  7 

between  facts,  or  involve  synthesis.  They  repre- 
sent the  mind  as  holding  two  or  more  objects  of 
consciousness  before  it  and  affirming  or  denying 
some  sort  of  connection  or  relation  between  them. 
When  I  see  or  think  of  an  object  I  conceive  it  per- 
haps as  a  group  of  attributes  or  as  belonging  to  a 
class.  In  one  case  I  perceive  it,  in  the  other  I  ap- 
perceive  it ;  the  former  denoting  the  process  of 
bringing  the  properties  to  inhere  in  the  same  sub- 
ject and  the  other  the  process  of  seeing  what  a 
thing  is.  In  both  I  compare  and  unify  experiences 
or  things.  Also  when  I  reason.  In  all  I  am  dis- 
covering relations  in  a  series  or  multiple  of  facts 
that  make  them  some  kind  of  definite  whole.  This 
may  be  made  clearer  by  considering  the  three  pro- 
cesses with  which  logic  is  concerned — Conception, 
Judgment,  and  Reasoning. 

(a)  Conception. — Conception  is  the  act  of  mind 
which  in  some  way  unites  facts  or  experiences  to 
form  definite  ideas.  The  product  may  be  called 
a  concept.  This  is  of  two  kinds:  (i)  Individual 
wholes  and  (2)  class  wholes.  The  former  may 
also  be  called  attribute  or  substance  wholes,  and 
the  latter  general  concepts.  But  the  individual 
whole  is  found  by  conceiving  a  group  of  attributes 
as  belonging  to  the  same  thing  or  subject.  It  is 
illustrated  most  clearly  by  a  proper  noun,  such  as 
"  Plato,"  "  Bucephalus,"  etc.  A  general  term  will 
also  represent  such  a  group  of  attributes,  usually 
if  not  always,  but  it  also  stands  for  more  than 
this  at  the  same  time.  A  class  whole  represents 
a  group  of  individuals,  thought  together  and  de- 
noted by  the  same  term  on  the  ground  of  common 


8  LOGIC    AND    ARGUMENT 

attributes.  Thus  "man,"  "quadruped,"  "tree," 
"animal, "are  concepts  that  denote  an  indefinite 
number  of  individuals  of  like  kind  and  applicable 
equally  to  each  individual  in  the  class.  They  are 
names  for  objects  grouped  together  distributively, 
as  it  is  called,  and  not  collectively,  by  an  act  of 
comparison  and  abstraction.  The  common  prop- 
erties are  noted  and  the  differences  are  ignored. 
But  in  both  kinds  of  concepts  an  act  of  synthesis 
takes  place.  In  individual  or  attribute  wholes  the 
synthesis  is  of  different  attributes  or  qualities  in  the 
same  thing  or  subject,  and  in  class  wholes  or  gen- 
eral concepts  the  synthesis  is  of  the  same  or  like 
qualities  in  different  things  or  individual  subjects. 
The  same  distinction  can  be  expressed  in  another 
way.  The  former  may  be  considered  a  group  of 
different  attributes  in  the  same  subject  or  indi- 
vidual, and  the  latter  a  group  of  different  indi- 
viduals or  subjects  with  similar  attributes,  only 
the  common  qualities  being  considered,  while  the 
differences  are  neglected.  The  acts  of  mind  in 
each  case  are  both  unifying  acts,  involving  a  judg- 
ment of  connection,  though  they  differ  in  respect 
of  the  object-matter  about  which  they  are  em- 
ployed. Both  seize  upon  the  constant  facts  or 
groups  of  facts  and  qualities  for  the  purpose  of 
giving  them  a  name  which  may  always  denote 
them  and  be  their  logical  equivalent  in  discourse. 
All  conceptions  whatsoever  may  fall  under  one  or 
the  other  of  these  forms.  No  exception  is  pos- 
sible until  a  subject  is  found  with  only  one  prop- 
erty, and  this  could  still  be  called  an  individual 
whole,  though  we  should  not  speak  of  a  synthesis 


INTRODUCTION  9 

of  different  qualities,   but  merely   the    idea  of  a 
single  quality  in  a  subject. 

(b)  Judgment. — Judgment  is  the  act  of  mind 
which  perceives  and  asserts  a  relation  between 
things.  It  may  be  a  relation  of  identity  or  differ- 
ence, of  agreement  or  disagreement,  an  affirmative 
or  a  negative  relation.  The  term  is  also  used  to 
denote  a  proposition  which  is  in  reality  the  prod- 
uct of  the  act.  But  here  the  emphasis  is  upon 
the  mental  act  which  connects  affirmatively  or 
negatively  objects  of  consciousness.  These  ob- 
jects will  be  attributes  and  subjects.  The  relations 
will  be  between  attributes  and  attributes,  subjects 
and  attributes,  and  subjects  and  subjects.  Thus 
I  may  affirm  or  deny  a  connection  between  various 
attributes,  or  between  various  subjects  and  attrib- 
utes, or  between  various  subjects.  For  instance, 
"  White  is  not  blue,"  "  Plato  is  wise,"  "  Men  are 
bipeds,"  or  "Lincoln  was  not  Socrates."  The  act 
of  judgment  involves  a  connection  or  exclusion 
which  cannot  always  be  expressed  by  a  single  term 
or  concept,  and  hence  is  often  defined  as  the  asser- 
tion of  agreement  or  disagreement  between  con- 
cepts. For  practical  purposes  this  definition  can 
be  accepted,  though  the  more  technical  account  of 
it  may  be  considered  in  order  to  evade  objections 
based  upon  the  desire  for  theoretical  completeness 
and  accuracy.  The  fact  that  most  judgments  in 
discourse  are  judgments  of  relation  between  in- 
dividual and  general  concepts,  as  defined  techni- 
cally, may  justify  the  reference  to  them  in  that 
form  as  typical  of  practical  usage,  and  we  may 
either  stretch  the  term  "concept  "  to  include  in- 


I0  LOGIC   AND    ARGUMENT 

dividual  attributes  as  such,  or  permit  the  action 
of  judgment  to  relate  or  connect  properties  that 
are  sometimes  called  percepts  or  individual  ob- 
jects of  apprehension  in  distinction  from  individ- 
ual and  class  wholes.  But  aside  from  the  question 
of  its  subject-matter  the  judgment  is  still  a  unify- 
ing act  or  assertion  of  relation  of  some  kind.  It 
represents  consciousness  as  looking  at  two  facts 
or  things  at  the  same  time,  and  pronouncing  upon 
this  agreement  or  disagreement,  likeness  or  un- 
likeness,  connection  or  disconnection  with  each 
other. 

(c)  Reasoning. — This  process  is  simply  a  little 
more  complex  in  its  object-matter  than  conception 
and  judgment.  It  is  still  an  act  of  discovering 
or  asserting  relations,  but  most  usually  between 
judgments,  though  it  may  be  involved  in  the  for- 
mation of  concepts  themselves.  In  usual  discourse, 
however,  it  is  the  movement  of  the  mind  from  one 
proposition  to  another  in  which  the  act  discovers 
and  asserts,  and  agreement  or  disagreement  be- 
tween relations  noticed  in  judgments.  Thus  if  I 
know  that  metals  have  a  metallic  lustre  and  am 
told  that  sodium  is  a  metal,  I  am  likely  to  infer 
that  sodium  has  a  metallic  lustre,  though  I  have 
not  seen  the  fact.  I  expect  to  find  this  fact  to  be 
true  on  the  fact  that  the  asserted  connection  be- 
tween sodium  and  metals,  on  the  one  hand,  and 
metals  and  lustre  on  the  other,  is  true.  The  in- 
ference or  reasoning  is  the  transition  to  connec- 
tions that  are  not  suggested  by  a  single  proposition 
in  this  case,  though  in  one  kind  of  reasoning  a 
new  order  of  connection  may  come  out  of  even  a 


INTRODUCTION  1 1 

single  statement.  But  in  all  cases  the  same  act  of 
noting  identity  and  difference,  agreement  and  dis- 
agreement as  in  judgment,  characterizes  reason- 
ing, only  the  matter  is  more  complex  than  in  the 
other  two  logical  processes.  It  is  a  process  which 
usually  or  always  affects  the  degree  of  certitude 
or  probability  in  regard  to  propositions  which  may 
not  carry  with  them  satisfactory  conviction  until 
this  relation  is  seen.  Consequently  it  becomes  a 
means  of  proof  and  discovery,  if  not  of  new  mat- 
ter of  knowledge,  then  of  new  relations  between 
known  facts. 

Logic  will  then  have  to  do  with  the  laws  that 
regulate  the  formation  and  correct  use  of  concep- 
tions, propositions,  and  reasonings,  the  processes 
involved  in  the  comparison  and  unification  of  ideas. 
Its  main  object  is  to  establish  conviction  when  it 
is  employed  as  an  art,  and  to  formulate  laws  for 
correct  thinking  when  it  is  a  science.  Its  scope, 
however,  covers  all  the  acts  of  mind  comparing 
and  connecting  phenomena  for  the  sake  of  know- 
ing their  relations  as  subject  to  constancy  and 
proof. 

III.  SCOPE  OF  DISCOURSE — The  general 
meaning  of  thought  expression,  as  comprehending 
every  kind  of  presentation  of  ideas,  has  already 
been  mentioned,  and  also  the  aspect  of  it  which 
will  come  under  notice  here.  We  found  it  to  rep- 
resent both  aesthetic  and  systematic  form,  and 
stated  that  only  the  latter  feature  would  be  in- 
cluded in  the  present  treatise,  as  the  field  for  the 
application  of  logical  as  distinct  from  literary  or 
rhetorical  method  proper.  That  is  to  say,  we 


12  LOGIC   AND   ARGUMENT 

intend  here  to  examine  the  principles  which  regu- 
late the  systematic  construction  of  discourse  as 
distinct  from  elegance  of  expression  or  of  forms 
designed  merely  to  please  the  feelings  of  taste. 
But  it  will  conduce  to  a  better  understanding  of 
our  purpose  if  we  briefly  sketch  the  whole  field  of 
idea  expression  comprising  the  literary,  historical, 
scientific,  and  philosophic  modes  of  thought.  We 
can  then  clearly  observe  the  limited  conception  to 
be  taken  of  discourse  for  our  purposes. 

ist.  Divisions  of  Idea  Expression. — The  expres- 
sion of  ideas  divides  itself  into  two  general  forms, 
namely  :  Poetry  and  Prose.  This  distinction  is 
based  merely  upon  the  mode  of  literary  and 
grammatical  construction.  Both  are  governed  by 
the  two  functions  of  rhetoric,  aesthetic  principles 
designed  to  please  the  feelings,  and  systematic 
principles  to  influence  the  intellect.  Each  divi- 
sion, however,  can  be  further  sub-divided  :  Poetry 
into  Didactic,  Lyric,  Epic,  and  Dramatic,  and 
Prose  into  the  Literary  or  Polite, and  the  Explana- 
tory. The  Literary  or  Polite  Prose  may  be  divided 
into  Oratory,  Essay,  and  Fiction,  and  the  Explana- 
tory into  History,  Science,  and  Philosophy.  The 
tabular  outline  below  gives  a  bird's-eye  view  of 
this  field. 

f  Didactic. 

f  Poetry  J  £>Tic- 
Epic. 

[  Dramatic. 

Thought  Products  . . .  •{  (  Oratory. 

f  Literary . . . .  -^  Essay. 

Prose..  \  \  ?*tion. 

f  History. 
(.  Explanatory.  \   Science. 

t  Philosophy. 


INTRODUCTION  13 

Now  the  conception  of  Discourse  as  it  is  here  to 
be  cultivated  will  cover  the  whole  field  of  Prose 
where  the  rules  for  systematic  construction  of 
thought  are  the  same  for  the  literary  as  for  the 
explanatory  forms  of  expression  ;  but  special 
reference  will  be  made  to  the  explanatory  branches 
of  idea  expression.  Perhaps  even  the  same  prin- 
ciples are  applicable  to  Poetry,  as  I  think  they  are  , 
but  as  we  are  not  considering  either  the  special 
principles  that  distinguish  poetry  as  such,  nor  the 
aesthetic  object  of  all  expression  we  may  limit  the 
idea  of  Discourse  or  systematic  construction  to 
Prose,  and  thus  keep  in  view  the  logical  side  of 
the  subject.  Hence  we  shall  speak  of  Discourse 
as  the  systematic  expression  of  thought,  and  illus- 
trate it  exclusively  for  the  field  of  prose,  ignoring 
that  aspect  of  rhetoric  which  has  aesthetic  expres- 
sion for  its  object. 

2d.  The  Functions  of  Discourse. — Discourse, 
like  logic,  has  an  object.  This  object  is  to  discuss 
and  present  a  theme.  The  theme  is  some  subject 
of  thought,  and  may  be  either  an  idea  or  a  truth, 
a  single  object  of  thought  requiring  analysis  and 
exposition,  or  a  proposition  requiring  demonstra- 
tion. The  object  to  be  served  by  discourse  will 
thus  have  a  range  limited  by  the  nature  of  the 
theme.  The  range  will  be  less  in  the  case  of 
an  idea  than  in  that  of  a  truth,  while  the  latter 
will  include  one  additional  function  and  all  that  is 
required  by  the  former.  An  idea  or  single  con- 
ception requiring  explanation  and  analysis  will  be 
any  individual  or  class  whole,  such  as  "metals," 
"cathedral,"  "architecture,"  "  art,"  "  science," 


14  LOGIC    AND    ARGUMENT 

"  Greece,"  "  Plato,"  "  British  Museum,"  "  The 
Papacy."  All  of  these  are  objects  to  be  described 
and  explained,  and  not  to  be  proved.  But  the 
second  class  of  conceptions  either  imply  judg- 
ments or  state  them,  and  in  addition  to  explana- 
tion require  proof.  They  are  concerned  with  the 
establishment  of  the  truth,  or  reality  of  an  idea  or 
proposition.  The  former  concerns  only  what  it  is, 
or  its  nature  as  an  admitted  or  conceivable  fact  ; 
the  latter  concerns  the  truth  of  some  law,  fact,  or 
principle  embodied  in  judgments.  The  proposi- 
tion may  not  always  be  expressed  formally.  It 
may  only  be  implied,  even  in  a  single  term,  as  in 
titles,  headlines,  etc.  But  a  theme  is  subject  only 
to  explanation  when  it  is  merely  a  conception,  in- 
dividual or  general,  and  becomes  subject  to  proof 
in  addition  to  explanation  only  when  it  expresses 
or  implies  a  proposition  to  be  affirmed  or  denied. 
Such  are  "  protection,"  "  free  trade,"  "  Malthus 
law  of  population,"  "  patent  laws,"  "single  tax," 
"punishment,"  "private  property,"  "the  impor- 
tance of  the  family,"  "  the  necessity  of  quarantine," 
"the  existence  of  God,"  "immortality,"  "the 
freedom  of  the  will,"  etc.  In  propositions  these 
conceptions  take  the  form,  "  protection  is  inde- 
fensible," or  "  protection  is  necessary,"  "  God 
exists,"  "  the  will  is  free,"  etc.  In  them  we 
have  judgments  whose  terms  are  to  be  explained, 
and  whose  assertions  are  to  be  proved  or  dis- 
proved, while  in  individual  conceptions  the  proc- 
ess stops  with  exposition.  The  whole  process 
of  discourse,  however,  of  logical  discourse,  as 
here  defined,  consists  of  two  fundamental  forms 


INTRODUCTION  1 5 

of  method  with  their  subordinate  divisions. 
They  are  Explanation  and  Confirmation.  Each  of 
these  can  only  be  briefly  outlined  at  this  stage  of 
the  work. 

ist.  Explanation. — The  explanation  of  a  theme 
is  the  exposition  of  the  characteristics  or  facts 
which  constitute  the  object  of  thought.  It  states 
what  a  thing  is  and  shows  all  the  qualities  or 
events  which  it  represents,  and  involves  two  gen- 
eral processes.  They  are  Analysis  and  Synthesis. 
Each  is  the  complement  of  the  other,  and  both 
processes  are  necessary  to  complete  the  process 
of  explanation. 

(a)  Analysis. — The  analysis  of  a  theme  is  the 
separation  of  a  conception  or  whole  of  thought 
into  its  constituent  parts,  qualities  or  relations, 
in  order  to  find  all  that  it  means  or  implies.  It  is 
a  process  that  discriminates  between  the  essential 
and  non-essential  attributes  expressed  by  a  thing. 
Its  object  is  to  render  clear  the  parts  that  make 
up  a  whole.  Three  processes  are  involved  in  it. 
They  are  Definition,  Division,  and  Partition.  The 
discussion  of  them  will  come  up  in  the  proper 
place. 

(If)  Synthesis. — Synthesis  is  a  constructive  proc- 
ess, and  consists  in  the  systematic  arrangement 
of  the  parts  of  a  whole  in  order  to  give  a  clear 
and  complete  conception  of  it  as  a  whole.  As 
analysis  shows  only  the  parts  that  constitute  a 
thing,  synthesis  shows  the  manner  in  which  those 
parts  constitute  an  orderly  whole.  Synthesis  ex- 
hibits a  coherent  totality,  a  finished  product,  and 
analysis  the  raw  material  out  of  which  it  is  com- 


!6  LOGIC   AND    ARGUMENT 

posed.  There  are  two  forms  of  synthesis,  ac- 
cording as  the  theme  or  object  of  thought  repre- 
sents a  space  whole,  or  a  time  whole.  They  are 
Description  and  Narration.  Both  are  processes  of 
systematization,  and  aim  to  give  an  orderly  ac- 
count of  the  qualities  or  facts  expressed  or  im- 
plied by  a  theme.  They  will  be  further  discussed 
at  another  time.  Possibly  Exposition  might  be 
added  as  a  third  form  of  synthesis,  for  what  may 
be  called  thought  wholes. 

ad.  Confirmation.  —  Confirmation  is  proof,  a 
process  of  establishing  conviction.  The  previous 
processes  only  show  what  a  conception  means,  or 
what  a  thing  is  :  they  do  not  determine  conviction. 
They  impart  instruction  as  to  facts  and  form  ideas 
of  real  or  possible  things,  but  they  do  not  aim  to 
dissolve  doubts,  to  decide  beliefs,  to  fix  the  truth 
or  falsity  of  propositions.  Proof  is  the  process 
by  which  the  truth  of  a  judgment  is  established. 
There  are  two  forms  of  this  proof  or  confirmation, 
according  as  it  determines  certitude  or  probability. 
They  are  Deductive,  or  Analytic,  and  Inductive,  or 
Synthetic  Proofs.  They  represent  the  reasoning 
processes  of  discourse,  and  are  superadded  to 
those  of  explanation.  They  also  will  come  up  for 
more  careful  exposition. 

IV.  SUMMARY — We  have  now  found  that 
logical  discourse  comprises  a  knowledge  of  the 
laws  of  thought  and  of  the  laws  of  constructive 
arrangement.  We  thus  combine  in  this  treatise 
the  practical  part  of  logic  and  the  logical  part  of 
rhetoric.  The  laws  of  thought  will  be  considered 
only  in  so  far  as  they  are  necessary  for  regulating 


INTRODUCTION  1 1 

the  correct  interpretation  and  use  of  conceptions, 
judgments,  and  reasoning,  and  the  principles  of 
rhetoric  will  be  considered  only  in  so  far  as  they 
deal  with  clear  and  systematic  treatment  of 
themes,  the  art  of  aesthetic  expression  being  left 
to  others  for  discussion.  Discourse  then,  as  it  is 
here  conceived,  denotes  the  logical  analysis  and 
synthesis  of  the  ideas  expressed  by  a  theme,  and 
all  subsequent  investigations  will  concern  the 
laws  and  conditions  under  which  those  processes 
can  best  be  applied. 


CHAPTER   II 
CLASSIFICATION   OF  TERMS   OR   CONCEPTS 

I.  DEFINITION   OF   TERMS.  --  The    words 
"  Term  "  and  "Concept  "  are  identical  in  logic,  but 
in  general  usage  their  synonymous  meaning  is  not 
so  apparent.    "  Term  "  has  a  grammatical  associa- 
tion and  generally  denotes  a  word,  while'  concept 
denotes  always  an  idea  of  some  kind.     In  logic, 
however,  a  term  is  any  word  or  words  that  con- 
stitute a  subject  of  thought.   Concept  denotes  the 
subject  of  thought  without  suggesting  so  distinctly 
the  word  by  which  it  is  named.    But  it  is  the  idea 
or  subject  of  thought  that  is   the  important  fact, 
and   this   may    be   expressed   either   by  a  single 
word,  or  by  any  combination  of  them  that  denotes 
a  single  idea.     For  instance,  "  the  Queen  of  Eng- 
land," "the  elderly  gentleman  in  the  box,"  are  as 
much  terms  in  logic  as  the  single  words  "  man," 
"  tree,"  "  house,"  etc.     Consequently  a  "  Term  " 
in  logic  may  even  be  a  whole  clause  or  phrase, 
provided  that  this  is  a  mere  adjunct  of  a  cen- 
tral  concept    which    it    designs    to   make   more 
definite. 

II.  DIVISION   OF  TERMS. —  The   classifica- 
tion of  terms  is  various,  inasmuch  as  there  are 
many  points  of  view  from  which  to  consider  them. 

18 


CLASSIFICATION    OF   TERMS    OR    CONCEPTS  19 

But  each  division  may  cover  all  the  terms  used  in 
discourse  or  having  importance. 

i  st.  Categorematic  and  Syncategorematic 
Terms. — This  division  is  based  upon  the  distinc- 
tion between  what  is  essential  and  what  is  not 
essential  to  the  formation  of  a  proposition. 

1.  Categorematic   terms   are   those   which   can 
stand  as  the  subject  or  predicate  of  a  proposition. 
They    are    of    three    kinds  :    (a)    substantive,   as 
"  horse,"  "  animal,"  "  government ;  "  (b)  adjectival, 
as  "  true,"  "generous,"  "  pertinent," and  (c)  verbal, 
as  "  shine,"  "  rule,"  "  assert." 

2.  Syncategorematic  terms  are  such  as  cannot 
stand  alone  as  subject  or  predicate  of  a  proposi- 
tion.    They  are  of  two  kinds  :  (a)  modal,  as  "  veri- 
ly," "amiably,"  "considerately,"  or  all  adverbs, 
and    (b)  relational,    as  "in,"  "by,"  "to,"  "and," 
"  through,"  or  prepositions  and  conjunctions. 

zd.  Singular  and  General  Terms. — This  divi- 
sion is  based  upon  the  distinction  between  Individ- 
ual and  Class  Wholes,  or  the  number  of  objects  to 
be  denoted  by  a  term.  Accordingly,  terms  in  this 
classification  are  distinguished  by  their  form  of 
extension,  a  property  to  be  considered  farther  on. 

i.  Singular  Terms  are  those  which  apply  in  the 
same  sense  only  to  a  single  object,  real  or  imag- 
inary. Proper  names  are  good  illustrations,  as 
"  Europe,"  "  Plato,"  "  Paris,"  though  any  term  not 
a  proper  name  but  denoting  only  a  single  whole, 
will  also  be  singular,  as  "  the  first  man,"  "  the 
highest  good,"  and  possibly  "  time,"  "  space,"  etc. 
A  combination  of  terms,  such  as  "  The  present 
Secretary  of  State,"  "  The  King  of  Spain,"  "  The 


2O  LOGIC   AND   ARGUMENT 

Superintendent  of  Public  Buildings,"  etc.,  will  also 
be  singular,  when  it  refers  only  to  one  specific 
person  or  thing.  Even  expressions,  like  "  this 
table,"  referring  to  an  individual  case  in  view,  or 
"  the  street  running  diagonally  across  the  city  of 
A,"  etc.,  are  singular  terms.  Some  seem  to  have 
thought  that  terms  like  "water,"  "stone,"  "  ice," 
"  mercury,"  "  iron,"  may  sometimes  be  singular, 
as  being  similar  to  "space,"  "time,"  "universe," 
but  I  should  treat  them  as  abstract  whenever  used 
to  denote  the  quality  or  qualities  which  make  the 
kind  of  thing  denoted  by  them.  Oneness  of  kind 
is  not  the  only  or  distinctive  feature  of  singular 
terms,  but  individuality,  or  singularity,  as  repre- 
senting a  concrete  individual  whole. 

2.  General  Terms  are  those  which  can  apply,  in 
the  same  sense,  to  each  individual  in  an  indefinite 
number  of  objects,  real  or  imaginary,  and  of  the 
same  kind.  They  are,  therefore,  terms  represent- 
ing class  wholes,  as  singular  terms  represent  indi- 
vidual wholes.  Illustrations  of  general  terms  are 
such  as  "man,"  "vertebrate,"  "animal,"  "  trees," 
"  figures,"  "  bipeds,"  etc.  In  these  instances  the 
terms  denote  more  than  one  object  and  apply  to 
all  of  the  same  kind.  Their  meaning  is  important 
in  the  interpretation  of  what  are  called  universal 
propositions. 

3d.  Collective  and  Distributive  Terms This 

division  is  based  upon  the  distinction  between  ag- 
gregate wholes  of  the  same  kind  and  class  terms. 
It  partly  coincides  with  the  division  into  singular 
and  general  terms,  the  latter  always  being  distrib- 
utive. 


CLASSIFICATION    OF    TERMS    OR    CONCEPTS  21 

1.  Collective   Terms  are  those  which  apply  to  an 
aggregate  whole  of  individuals,  usually  similar  in 
kind  and   constituting  together  a  totality  that   is 
spoken    of   as    if   it    were   an    individual.     Thus, 
"army,"  "forest,"  "crowd,"  "  nation,"  "  family," 
"  regiment,"  are  collective  terms  because  they  de- 
note composite  or  aggregate  wholes. 

2.  Distributive  Terms  are  those  which  apply  to 
each  individual  in  a  class,  or  to  a  single  individual. 
For  example,  "  man,"  "  vertebrate,"  "  quadruped," 
"  book,"  "  Germans,"  are   distributive  terms.     It 
will  be  remarked  also  that  they  are  general  terms. 
But  even  singular  terms  are  distributive,  as  "  Bis- 
marck," "  Pitt,"  etc.    Consequently,  "  distributive" 
expresses  individual  denotive   power  as   distinct 
from  composite,  while  singular  and  general  dis- 
tinguish between  one  and  more  than  one  object 
of   thought,    whether   collective   or    distributive. 
Hence  we  find  the  division  between  singular  and 
general  terms  crossing  between  that  of  collective 
and  distributive.     Thus  some  singular  names  or 
terms  are  collective,  as  "  The  Vatican   Library," 
"The    72d    Regiment,"    "The    French     nation," 
while  also  all  collective  terms  not  singular  and 
applicable  to  an  indefinite  number  of  similar  ag- 
gregates are  general  and  therefore  are  distributive 
at  the  same   time  that  they  are  collective.     But 
they  are  not  distributive  in  the  same  sense  that 
they  are  collective. 

It  is  important  also  to  keep  clear  the  distinction 
between  class  wholes  and  collective  wholes,  or  the 
distinction  between  distributive  and  the  collective 
functions  of  the  same  or  different  terms.  They 


22  LOGIC    AND    ARGUMENT 

are  often  confused  so  as  to  call  a  term  denoting  a 
class  a  collective  term.  But  the  radical  difference 
is  that,  besides  denoting  more  than  one,  collective 
terms  name  a  whole  spoken  of  as  one  object, 
while  class  or  general  terms  denote  both  more 
than  one  and  apply  to  each  individual  in  the  class. 
Collective  terms  do  not  apply  to  the  units  com- 
posing the  aggregate.  The  relation  between  the 
two  divisions  may  be  summarized  in  the  follow- 
ing tabular  form  : 


Terms 


or  Terms 


i  Distributive  only  <-  it     »•  )  Singula 

General  j  Collective  and  fSistributive       [  CollecUve      ^  GeSera 


4th.  Concrete  and  Abstract  Terms.— It  is  much 
more  difficult  to  define  concrete  and  abstract 
terms  satisfactorily,  because  the  current  and  tra- 
ditional accounts  of  them  show  less  agreement 
than  in  the  previous  cases.  But  the  general  dis- 
tinction is  based  upon  the  difference  between  any- 
thing considered  alone,  and  out  of  relation  to  its 
individual  subject.  There  are  also  terms  that 
have  both  a  concrete  and  an  abstract  signification. 

i.  Concrete  Terms  are  those  which  stand  for  a 
thing  thought  and  used  as  a  subject  of  properties, 
or  for  an  attribute  thought  and  used  as  an  attri- 
bute, but  in  each  case  conceived  independently 
and  alone.  This  definition  provides  for  two 
kinds,  certain  nouns  and  all  adjectives.  Thus 
"  Parthenon,"  "  Lincoln,"  "  Charter  Oak,"  and 
"  wise,"  "  noble,"  "  clear,"  etc.,  are  concrete  terms 
or  conceptions. 


CLASSIFICATION    OF    TERMS    OR    CONCEPTS  23 

2.  Abstract  Terms  are  those  which  represent  an 
attribute   conceived   apart   from   the    subject    to 
which  it  belongs,  and  treated  as  if  it  were  a  sub- 
ject itself.    Thus,  "  righteousness,"  "  ability,"  "  vir- 
tue," "purity,"  "  redness,"  are  abstract  concepts 
or  terms.     These  are  used  as  nouns  and  can  be- 
come subjects  of  propositions,  while  the  attributes 
they  express  can  only  be  predicates. 

3.  Subdivisions. — Some  terms  are  only  concrete, 
some  are  only  abstract,  and  some  may  be  either 
concrete  or  abstract.     This  fact  gives  rise  to  the 
distinction  between ///r^  and  mixed  terms.     Then, 
as  concrete  terms  may  be  either  substantives  or 
adjectives,  we  may  recognize  two  kinds  of  this 
class  and  two  kinds  of  the  abstract.     The  follow- 
ing table  or  outline  with  illustrations  will  indicate 
what  is  meant  while  it  explains  the  definitions  : 

(  (  r  j  Substantive=Singular  Nouns,  e.g.,  Homer. 

p  ete"1  Attributive=  Adjectives,  e.?.,  Pure. 

Terms  •(        lre  '  1    Au_f_.,rt      1  Static= Adjectival  Nouns,  e.g..  Sweetness. 
act"  1  Dynamic  =  Verbal  Nouns,  e.g.,  Distillation. 
(_  Mixed  =  Concrete  and  Abstract,  e.g.,  Government,  Religion,  etc. 

Certain  kinds  of  terms  are  omitted  from  the 
illustrations  in  this  outline.  They  are  such  gen- 
eral terms  as  "man,"  "tree,"  "animal,"  "  build- 
ing," etc.  The  reason  for  this  omission  is  that 
some  writers  treat  them  as  concrete.  But  this  is 
due  to  a  conception  of  the  concrete  which  is  not 
the  logical  one  and  which  will  come  up  for  con- 
sideration in  a  moment.  I  regard  them,  however, 
as  both  concrete  and  abstract,  and  hence  as  belong- 
ing to  the  mixed  class  along  with  "government," 
"  religion,"  etc.,  and  for  the  same  reason.  All 


24  LOGIC   AND    ARGUMENT 

general  terms,  in  fact,  may  be  treated  as  abstracts, 
though  it  may  not  be  true  that  all  abstract  terms 
are  general.  But  general  terms  are  abstract  when 
they  stand  only  for  the  common  properties  of  the 
individuals  composing  the  class,  and  concrete 
when  they  denote  the  individuals  as  such.  Thus, 
in  the  use  of  a  distinction  still  to  be  explained, 
general  terms  are  abstract  when  they  are  taken  in 
their  intension  or  to  denote  the  qualities  expressed 
by  them,  and  concrete  when  they  are  taken  in 
their  extension  or  to  denote  the  number  of  individ- 
uals in  the  class. 

4.  The  Popular  Distinction. — The  popular  con- 
ception of  concrete  terms  is  that  of  sensible  ob- 
jects, and  of  abstract  terms  as  that  of  non-sensible 
things.  This  notion  coincides  with  the  difference 
between  material  and  immaterial  things.  From 
this  point  of  view  "man,"  "tree,"  "Plato,"  "Bis- 
marck," "  nation,"  "  white,"  "  round,"  "  heavy," 
would  all  be  concrete,  and  "thought,"  "emotion," 
"spirit,"  "government,"  "religion,"  "generous," 
"sincere,"  etc.,  would  be  abstract.  But  while  this 
distinction  may  do  very  well  for  the  purpose  of 
indicating  the  difficulties  involved  in  imparting 
our  ideas  of  non-sensible  things,  it  does  not  serve 
the  purposes  of  clear  logical  thinking.  The  com- 
mon mind  may  find  it  easier  to  deal  with  tangible 
or  sensible  things,  but  the  propositions  and  beliefs 
we  form  have  as  much  to  do  with  the  non-sensible 
as  the  sensible,  and  hence  the  distinction  for  logic 
between  the  concrete  and  the  abstract  must  be 
between  facts  conceived  as  self-sufficient  and  facts 
conceived  out  of  relation  to  their  subject,  and  not 


CLASSIFICATION    OF    TERMS    OR    CONCEPTS  25 

between  the  representable  or  picturable  and  the 
non-representable  or  unpicturable.  Errors  in  ar- 
gument do  not  occur  from  the  confusion  of  the 
intangible  with  the  tangible,  but  from  the  illegiti- 
mate transition  from  a  fact  out  of  relation  to  its 
subject,  or  vice  versa,  and  hence  it  is  this  distinc- 
tion which  logic  must  keep  in  view. 

5th.  Positive  and  Negative  Terms. — This  divi- 
sion is  based  upon  the  distinction  between  terms 
that  imply  the  presence  and  those  that  imply  the 
absence  of  an  attribute.  From  the  position  of 
grammatical  form  in  connection  with  meaning  we 
may  recognize  also  Privative  and  Nego-positive 
terms  or  concepts,  as  will  be  further  explained, 
but  considering  "  terms  "  and  "  concepts  "  as 
identical  we  may  reduce  the  four  forms  to  two, 
and  divide  each  of  the  two  into  pure  and  mixed. 
This  may  be  represented  after  the  definition  of 
each. 

1.  Positive   Terms  are   those  which  signify  the 
presence    or   possession    of   certain    qualities  de- 
noted by  the  word  ;  for  example,  "  good,"  "  pure," 
"excellence,"  "metal,"  "  organic,"  "  human,"  etc., 
are  positive  terms.     They  are  positive  grammat- 
ically and  logically,  or  both  in  form  and  matter. 

2.  Negative   Terms  are  those  which  denote  the 
absence  of  certain  given  qualities ;  as  "  inorganic," 
"insincere,"  "imperfect,"    "headless,"    "unnatu- 
ral," etc.     These  are  negative  in  both  form  and 
matter.     The    usual    symbols   of   negative  terms 
are  in,  tin,  less,  dis,  a  or  an,  anti,  mis,  sometimes 
de,  and  non,  and  not. 

3.  Privative  Terms  are  those  which  signify  the 


26  LOGIC   AND    ARGUMENT 

absence  of  a  quality  or  qualities  once  possessed 
or  belonging  normally  to  the  object  named.  Thus 
"deaf,"  "dead,"  "dumb,"  "blind,"  "dark,"  etc., 
are  privative  terms.  They  are  positive  in  form 
and  negative  in  matter  or  meaning. 

4.  Nego-positive  Terms  are  those  which  denote 
the   presence    of   a   positive   quality    though  ex- 
pressed  in   a   negative   manner ;   as  "  inhuman," 
"  disagreeable,"     "  infamous,"     "  inconvenience," 
"  displeasure,"  "  invaluable,"  etc.    They  are  nega- 
tive in  form  and  positive  in  matter.     They  can, 
in  most  cases  at  least,  be  distinguished  from  nega- 
tive conceptions  or   terms,  pure  and  simple,  by 
substituting    their   positive    equivalents.       Thus 
"  unhappiness"     and     "invaluable"    have     their 
equivalents  in  the  positive  terms  "  misery  "  and 
"costly."      Some   terms  may   be  interpreted   in 
either  a  negative   or  a   nego-positive   sense,  ac- 
cording as  we  choose  to  use  them.     Thus  "  un- 
certain," "  unhealthy,"  "  unpleasant,"  "  indistinct," 
may  be  conceived  as  the  negatives  of  "  certain," 
"  healthy,"    "  pleasant,"    "  distinct,"    or,   as    the 
nego-positive  equivalents  of  "doubtful,"  "sickly," 
"painful,"  "obscure." 

5.  Summarized   Divisions.  —  The    last    remark 
shows  that  there  may  be  a  grammatical  difference 
in  the  form  of  terms,  but  no  logical  difference  in 
meaning  or  matter.     It  will  be  possible,  therefore, 
to  reduce  the  fourfold  division  of  terms  as  here 
defined  and  based  partly  upon  grammatical  and 
partly   upon    logical    principles,    to   two    classes, 
based  only  upon  logical  principles.     They  will  be 
viewed    wholly  from   the   standpoint  of  concepts, 


CLASSIFICATION    OF    TERMS    OR    CONCEPTS  2^ 

which  are  logical  in  their  implication,  and  not 
from  that  of  terms,  which  have  a  grammatical 
association.  Hence  we  may  ultimately  reduce  all 
concepts,  or  terms  in  meaning,  to  two  classes,  the 
positive  and  negative,  making  the  privative  nega- 
tive and  the  nego-positive,  positive,  though  for 
the  sake  of  clearness  calling  attention  to  their 
mixed  character  from  the  standpoint  of  gramma- 
tical structure  as  compared  with  their  meaning. 
This  is  only  to  say  that  the  grammatical  and  the 
logical  criteria  of  the  nature  of  terms  are  not 
always  coterminous.  Each  taken  alone  will  give 
us  two  divisions,  positive  and  negative,  but  when 
terms  come  to  be  arranged  under  these  divisions 
some  that  would  be  positive  grammatically  would 
be  negative  logically,  and  some  that  would  be 
negative  grammatically  would  be  positive  logi- 
cally. We  may,  therefore,  outline  in  tabular  form 
the  various  ways  of  classifying  and  defining  terms 
or  concepts  as  just  discussed. 


(Positive  =  Positive  in  both  form  and  matter. 
Negative  =  Negative  in  both  form  and  matter. 
Privative  =  Positive  in  form  but  negative  in  matter. 
Nego-positive  =  Negative  in  form  but  positive  in  matter. 

f  Positive  =  Grammatical  and  Logical  forms  cotermi- 
Pure    -1  nous. 

|  Negative  =  Grammatical  and  Logical  forms  cotermi- 


nous. 


Terms  or 

f  Privative  =  Grammatically   positive   and     Logically 


Mixed  -I  negative. 

]  Nego-positive  =  Grammatically  negative  and  Logi- 
cally positive. 

f  Positive      -|  Dimple  =  £ure  Positive 
Concepts    •( 

Negative    •}  Simple  =  Pure  negative. 
I      °         "(  Complex  =  Privative. 


2g  .     LOGIC   AND    ARGUMENT 

6.  Infinitated  Terms. — There  is  a  form  of  con- 
ception which  is  called  "  infinitated."  This  term 
is  applied  to  such  conceptions  because  it  refers 
to  that  use  of  them  which  denotes  the  thought  of 
all  other  things  than  those  expressed  by  the  cor- 
responding positive  term.  It  avails  to  divide 
all  possible  objects  of  thought  into  two  classes. 
These  classes  may  be  called  the  positive  and  the 
negative,  as  above.  The  negative  may  be  called 
the  infinitated  concepts.  The  usual  symbol  of  such 
terms  is  non  and  not,  as  "  non-moral,"  "non-ma- 
terial," "  not-animal,"  "  not-tree,"  etc.  They  are 
not  always,  if  ever,  recognized  as  rhetorically  ele- 
gant, but  are  valuable  often  to  make  clear  the 
really  negative,  or  infinitatively  negative  nature 
of  the  idea  in  mind.  Thus  "  tree  "  and  "  not-tree  " 
will  together  comprise  all  objects  of  thought  and 
in  some  logical  processes,  as  dichotomous  division, 
obversion  and  contraversion,  to  be  considered 
later,  it  is  important  to  have  this  fact  known. 
Every  term  then,  conceived  or  expressed  by  the 
qualification  non  or  not,  and  denoting  the  whole 
universe  of  objects  excluded  from  the  positive 
concept  is  an  infinitated  conception.  Even  such 
terms  as  "not-just,"  "not-good,"  "non-moral," 
or  perhaps  all  negative  terms,  can  be  conceived  in 
an  infinitated  sense,  and  sometimes  are  so.  But 
in  common  usage  negative  adjectival  or  attribu- 
tive concepts  are  applied  to  the  same  general  kind 
of  subject  as  the  positive,  and  no  reference  is 
made  or  understood  to  objects  outside  this  par- 
ticular limit.  Thus,  "  not-just  "  would  be  con- 
fined to  the  universe  of  actions,  this  being  divided 


CLASSIFICATION    OF    TERMS    OR    CONCEPTS  29 

into  "just  "and  "not-just  actions,"  other  things 
than  actions  not  being  implied  or  included  in  "  not- 
just,"  and  the  infinitation  not  extending  beyond 
the  negative  facts  within  the  concept  "  action." 
The  source  of  equivocation  from  this  may  be  dis- 
cussed again.  But  the  wider  meaning  of  infinita- 
tion is  clearer  when  applied  to  substantive  terms. 
6th.  Absolute  and  Relative  Terms — This  di- 
vision is  based  upon  the  distinction  between  in- 
dependence and  dependence  on  other  terms  for 
meaning.  In  its  narrower  import  the  distinction 
is  not  very  important  for  practical  logic,  though 
the  wider  use  of  it,  largely,  if  not  wholly  coincid- 
ing with  that  between  Concrete  and  Abstract  con- 
cepts, has  very  great  value.  Assuming  the  latter 
as  sufficiently  considered,  we  may  be  content  with 
a  very  brief  account  of  the  former. 

1.  Absolute  Terms  are  those  in  which  the  proper- 
ties or  qualities  expressed  are  intrinsic  to  the  in- 
dividual subject  and  do  not  represent  a  mere  rela- 
tion to  any  other  subject  or  being.     Thus  "  man," 
"  tree,"  "earth,"  "star,"  "  book,"  may  be  consid- 
ered as  absolute  terms.     They  do  not  imply  any 
necessary  correlatives  to  complete  their  meaning. 
The  things  which  they  denote  may  exist  in  all 
sorts  of  relations,  but  it  may  not  be  necessary  to 
think  of  these  relations  in  order  to  obtain  an  ad- 
equate idea  of  what  the  term  means.     Quite  the 
contrary  terms  is  true  of  relative. 

2.  Relative  Terms  are   those   whose  distinctive 
meaning  is  derived   from   the  relation   expressed 
to  some  other  individual  object.     Thus  "  father," 
"son,"    "parent,"    "master,"    "servant,"    "  mon- 


30  LOGIC   AND    ARGUMENT 

arch,"  "  subject,"  etc.,  are  relative  terms.  Each 
term  suggests  a  relation  to  others  as  the  distinc- 
tive meaning  of  the  word.  Thus  "  father  "  is  a 
"  man,"  but  a  man  in  a  certain  relation,  and  the 
term  is  intended  to  express  that  relation,  which 
may  not  be  a  quality  necessary  for  recognition  of 
the  individual  as  such.  We  see  in  this  way  that 
relative  terms  suggest  the  thought  of  other  indi- 
viduals with  the  relation  involved  as  a  part  of  the 
term's  meaning,  while  absolute  terms  suggest  only 
the  qualities  in  the  subject  without  a  relation  to 
others  being  necessarily  involved. 


CHAPTER   III 
THE    CONTENT    OF    TERMS 

i.  INTRODUCTION.— Every  term  or  concept 
has  a  content.  This  content  is  its  meaning.  As 
a  term  it  is  simply  a  word,  a  sound,  a  vocable,  but 
it  stands  for  something.  It  is  a  name  for  a  thing, 
a  fact,  a  quality  or  any  circumstance  about  which 
consciousness  or  knowledge  can  be  occupied.  As 
a  concept  it  is  an  idea  which  contains  a  reference 
to  the  same  that  is  denoted  by  a  word.  The  mean- 
ing or  content  is  simply  the  character  or  charac- 
ters which  a  term  names  or  implies,  or  which  an 
idea  represents. 

But  the  meaning,  material  content  and  ways  of 
viewing  a  term  are  rich  and  various.  All  of  them 
have  a  quantity  and  a  quality  import ;  that  is,  a 
reference  to  number  and  a  reference  to  properties. 
These  characteristics  bear  an  important  relation 
to  the  laws  of  thought  and  the  art  of  discourse. 
Different  principles  have  to  be  considered  in  treat- 
ing of  these  two  aspects  in  which  terms  may  be 
taken,  especially  when  we  come  to  treat  of  propo- 
sitions. But  at  present  we  are  limited  to  their  im- 
portance in  terms. 

The  aspects  under  which  concepts  have  always 
31 


32 


LOGIC   AND    ARGUMENT 


been  considered  by  students  of  logic  have  been 
expressed  by  the  \.&m  predicables,  borrowed  from 
Aristotle,  and  expressing  the  nature  of  the  "  predi- 
cates "or  attributes  possessed  by  terms.  They 
are  the  most  general  conceptions  under  which  the 
meaning  of  terms  can  be  described  and  have  been 
given  as  five  in  number.  I  hope  to  show  that 
they  are  reducible  to  four,  with  a  subdivision  of 
two  of  them  which  has  an  interest  outside  of  the 
mere  quantity  and  quality  import  of  terms.  But 
I  shall  first  give  the  old  table  of  predicables,  fol- 
lowing it  with  a  new  one. 

OLD  TABLE.  NEW  TABLE. 

Genus  (yivot)  =  Genus.  Genus  =  Genus. 

Species  (et&x)  =  Species.  Species       .    =  Species. 

Differentia  (Suwfropa)  =  Difference.  Conferentia  =  Identity. 

Proprium  (iti&v)  =  Property.  Differentia    —  Difference. 

Accidens  (<ni>i/3<:/3»i<co«)  =  Accident. 

To  the  new  table  I  might  add  Essentia  and  Ac- 
cidentia,  or  Essence  and  Accident,  but  I  regard 
them  as  subdivisions  of  Conferentia  and  Dif- 
ferentia. The  new  table,  however,  enables  us  to 
classify  the  "  predicables,"  or  ways  of  looking  at 
terms,  according  to  their  quantitative  and  their 
qualitative  meaning.  The  Genus  and  the  Species 
are  names  for  that  view  of  concepts  which  regards 
them  in  their  quantitative  power  or  meaning,  and 
Conferentia  and  Differentia,  in  their  qualitative 
power  or  meaning.  This  will  be  made  clearer  in 
the  discussion.  The  following  outline  will  show 
their  relations  to  each  other  and  to  Essentia  and 
Accidentia. 


THE    CONTENT   OF    TERMS  33 


f  Quantitative    j  Genus. 
(Extension).    {  Species. 


Content  of  Terms.  4  \  Conferentia.  \  Essentia. 

Qualitative    '  1  Accident* 


|  •  ^'  UtJ.ll  till  1  \   ^  I 

(Intension).  1  ,  F 

[Differentia.    {%£££ 


II.  EXPLANATION  OF  THE  PREDICABLES. 

— Before  we  enter  upon  the  discussion  of  the 
analysis  of  terms  or  concepts,  which  is  a  process 
of  determining  the  nature  and  range  of  their 
meaning,  it  will  be  necessary  to  define  and  explain 
the  meaning  of  the  predicables,  and  to  show  the 
relation  which  they  bear  to  each  other.  They  all 
refer  to  the  content  of  conceptions,  and,  as  indi- 
cated, are  reducible  to  two  general  ways  of  con- 
ceiving the  meaning  of  terms  ;  namely,  their  num. 
ber  significance,  which  is  called  their  extension,  and 
their  attribute  significance  which  is  called  their 
intension.  Each  of  these  properties  of  terms  must 
be  taken  up  in  its  order. 

ist.  Extension. — The  extension  of  a  term  is 
that  property  by  which  it  denotes  the  number  of 
objects  expressed  by  it.  This  extension  does  not 
imply  any  definite  number  of  objects,  but  names 
only  the  quantitative  capacity  of  a  term.  The  prop- 
erty is  best  illustrated  by  class  wholes  or  general 
terms,  as  "  man,"  "  Caucasian,"  "  animal,"  though 
singular  terms  have  it,  but  in  a  less  degree.  Terms 
which  compare  a  wider  and  narrower  meaning 
indicate  most  clearly  what  is  meant  by  the  prop- 
erty, as  "  man  "  and  "  biped."  "  Man  "  denotes  rela- 
tively fewer  individuals  than  "  biped  "  and  there- 
3 


34 


LOGIC   AND    ARGUMENT 


fore  has  less  extension,  or  denotes  a  less  number. 
This  gives  rise  to  two  forms  of  expressing  the 
relative  differences  in  extension  or  quantitative 
import  of  terms.  They  are  Genus  and  Species. 

1.  Genus. — Genus  is  a  term  which  expresses  the 
power  of  a  class  or  general  concept  to  include  in 
it  a  narrower  class  of  individuals  or  a  number  of 
individuals  not  grouped  in  classes.     More  briefly, 
genus  describes  every  term  which  denotes  a  class 
whole  of  any  kind.     Thus  "  man  "  is  a  genus  con- 
cept, because  it  is  a  name  which  applies  to  the 
various  classes  or  individuals  of  the  race  included 
under   it.     "  Substance  "    is   a   genus,  because  it 
includes    under  it  iron,   clay,  brass,  gold,  silver, 
water,  etc. 

2.  Species. — Species   is   a    term    which    denotes 
either  a  narrower  class  or  an  individual  compre- 
hended in  a  genus  or  wider   class.     It   has   less 
quantitative  meaning  than  genus.     Thus  "  Cauca- 
sian "  is  a  species  of  "  man,"  "  iron,"  of  "  metal," 
a  " triangle,"  of  "figure,"  etc.     According  to  the 
definition  also  "  Plato,"  "  Burke,"  and  all  similar 
singular  terms  will  be  a  species  of  "man."     It  will 
be  apparent  that  the  term  has  a  somewhat  differ- 
ent meaning  from  that  which    we   often  find    in 
Natural   History.     It  is  the  same  with  the  term 
genus.     But   the   doctrine  of   evolution    shows  a 
tendency  to   break   down  the  fixed   and   definite 
conception  of  them  current  in  science  previous  to 
it,  and  hence  they  have  become  both  of  them  more 
elastic.     This  tendency  therefore  approaches  more 
and  more  the  logical  and  relative  conception  of  the 
two  terms.     This  requires  a  brief  consideration. 


THE    CONTENT    OF    TERMS  35 

3.  Relation  of  Genus  and  Species. — The  illustra- 
tions suggest  the  fact  that  genus  and  species  are 
purely  relative  terms.  Thus  we  find  that  "  metal  " 
is  a  genus  compared  with  "iron,"  "gold,"  "sil- 
ver," etc.,  which  are  its  species,  but  is  a  species 
when  compared  with  "matter,"  or  "substance," 
which  are  its  genera.  To  make  this  more  general, 
we  notice  that  a  term  is  always  a  genus  in  relation 
to  a  narrower  extension,  and  a  species  in  relation 
to  a  wider  extension.  We  may  thus  proceed  in 
either  direction  until  we  reach  the  limits  of  farther 
progress,  as  "existence,"  "substance,"  "being," 
"vertebrate,"  "man,"  "American,"  "Lincoln." 
Here  in  this  example,  all  intermediate  terms  be- 
tween the  two  extremes  are  either  genera  or 
species,  according  as  they  are  conceived  in  rela- 
tion to  a  higher  or  a  lower  order ;  according  as  they 
include  a  lower,  or  are  included  in  a  higher  class. 
Thus  "American"  is  a  genus  to  "  Lincoln,"  and 
a  species  to  "man,"  etc.  But  "the  two  extremes 
cannot  be  viewed  in  this  twofold  relation.  "  Ex- 
istence "  is  a  genus,  but  not  a  species,  and  "  Lin- 
coln "  is  a  species  and  not  a  genus.  The  former 
is  not  a  species,  because  it  cannot  be  brought 
under  a  wider  class  of  objects,  and  the  latter  is 
not  a  genus  because  it  cannot  be  divided  into 
lower  species  or  individuals.  All  singular  terms 
are  species  and  not  genera,  and  are  called  the 
infiina  species,  or  lowest  species.  They  are  always 
individuals. 

On  the  other  hand  the  highest  genus,  because 
not  a  species,  is  called  the  sum  mum  genus  or  genus 
generalissimum.  It  is  represented  by  some  such 


^6  LOGIC    AND    ARGUMENT 

term  as  "existence,"  "thing,"  "something,"  "ul- 
timate reality,"  "  the  absolute,"  or  even  "  being  " 
in  its  widest  sense,  but  in  all  cases  must  be  thought 
as  a  single  concept.  It  is  thus  worthy  of  remark 
that  there  is  in  reality  but  one  summum  genus, 
while  there  may  be  an  indefinite  number  of  infima 
species.  All  intermediate  terms  between  these  ex- 
tremes are  sometimes  called  subalterns,  as  being 
either  genera  or  species,  according  to  the  relation 
in  which  they  are  viewed. 

An  important  fact  also  to  remark  is  that  genus 
and  species  represent  concepts  in  a  certain  rela- 
tion of  agreement  with  each  other.  The  genus  al- 
ways includes  the  species,  and  each  species  includes 
a  part  of  the  genus,  while  the  species  mutually 
exclude  each  other  ;  that  is,  the  terms  denoting 
them  are  always  opposed  to  each  other. 

It  will  be  necessary  to  notice  again  and  a  little 
more  fully  the  use  of  the  terms  genus  and  species 
in  Natural  History.  A  species  is  there  "  a  class  of 
plants  or  animals  supposed  to  have  descended 
from  common  parents,  and  to  be  the  narrowest 
class  possessing  a  fixed  form  ;  a  genus  is  the  next 
higher  class."  This  is  Jevons's  definition,  but  he 
does  not  illustrate  it.  Perhaps  we  could  say  that, 
in  Natural  History,  the  term  "tree  "  would  repre- 
sent a  genus,  and  "oak,"  "elm,"  "maple,"  etc., 
would  represent  z.  species,  while  "  red-oak,"  "  white- 
oak,"  "black-oak,"  etc.,  would  be  varieties.  But 
the  peculiar  use  of  the  term  species  here  is  that  it 
is  supposed  to  be  fixed,  and  not  relative  as  in 
logic,  where,  as  we  have  seen,  any  but  the  summum 
genus  and  the  infima  species  may  be  either  a  genus 


THE    CONTENT    OF    TERMS  37 

or  a  species,  according  to  its  relation  to  a  higher 
or  lower  order.  In  natural  history,  however, 
species  is  supposed  to  represent  certain  fixed 
characters  and  relations  to  a  common  progenitor. 
But  the  acceptance  of  the  doctrine  of  evolution 
prevents  the  drawing  of  any  such  determinate 
line  of  distinction,  except  arbitrarily.  In  this  doc- 
trine, founded  upon  the  variability  of  "  species," 
the  conception  becomes  elastic  and  indistinct,  de- 
noting only  certain  characteristics  different  from 
the  genus.  Hence  the  change  approximates  the 
logical  import,  and  may  ultimately  make  them 
identical. 

2d.  Intension. — The  intension  of  a  term  is  its 
power  to  denote  qualities.  Every  term  not  only 
implies  a  certain  number  of  things,  whether  sin- 
gular or  general,  but  it  also  stands  for  certain 
qualities  or  properties  which  belong  to  the  thing 
named.  For  instance,  the  term  "  man  "  is  not 
only  a  name  for  a  certain  indefinite  number  of  in- 
dividuals to  which  the  word  applies,  but  it  is  also 
a  name  for  the  group  of  qualities  or  attributes 
which  constitute  these  individuals.  It  denotes  a 
certain  form,  stature,  habits,  intelligence,  moral 
character,  etc.  These  qualities  make  the  individ- 
ual man.  The  intension  of  the  term  is  only  a 
name  for  the  qualities  for  which  the  term  stands. 
They  are  also  called  the  properties,  attributes, 
characteristics  of  that  to  which  they  belong. 
Every  term  names  or  implies  at  least  a  certain 
number  of  them,  as  "  mountain,"  "  horse,"  "vir- 
tue," "religion,"  "car,"  "metal,"  "whiteness," 
"  Bucephalus."  Hence  this  power  to  denote  qual- 


38  LOGIC   AND   ARGUMENT 

ities  in  a  term  is  called  its  qualitative  power  or 
intension,  which  in  common  English  is  its  func- 
tion to  indicate  or  imply  the  properties  possessed 
by  the  thing  named.  In  the  arrangement  of 
things  and  events  according  to  genera  and  species 
it  is  found  to  be  necessary  to  distinguish  these 
properties  into  two  kinds,  which  I  shall  call  the 
Conferentia  and  the  Differentia.  This  shows  a  dis- 
tinction between  the  kinds  of  intension  or  proper- 
ties expressed  by  concepts.  Each  must  be  defined 
and  examined  in  its  order. 

i.  Conferentia. — Conferentia  is  the  name  for 
the  common  qualities  expressed  by  a  general  or 
class  term.  Thus  the  concept  "  tree,"  considered 
in  respect  of  its  intension  alone,  or  the  properties 
denoted  by  it,  represents  those  common,  some- 
times called  universal,  qualities  found  in  all  the 
individuals  of  the  class  :  for  instance,  its  woody 
structure,  truncated  form,  possession  of  leaves 
and  branches,  capacity  for  growth,  etc.  Another 
illustration,  as  "  Americans,"  shows  vertebrate 
structure, complexion,  stature,  citizenship  or  birth- 
place, etc.,  are  the  common  facts  expressed  by  the 
term.  Conferentia  thus  names  the  qualities  that 
make  the  class,  and  is  only  a  technical  term  for 
what  are  called  the  common  or  universal  proper- 
ties of  the  group  of  individuals  expressed  by  gen- 
eral terms.  Essence  or  essential  properties  are 
expressions  sometimes  used  for  the  same  fact. 
But  as  I  propose  to  distinguish  between  what  is 
universal  or  conferential  as  a  fact  from  what  may 
sometimes  be  called  essential,  I  shall  not  make  the 
terms  exactly  equivalent. 


THE   CONTENT   OF    TERMS  39 

The  term  "  conferentia  "  is  synonymous  with 
one  meaning  of  the  term  "genus  "  ;  namely,  that 
in  which  it  is  contrasted  with  differentia.  There 
are  two  pairs  of  contrasts  in  which  the  term 
"  genus  "  appears.  One  is  "  genus  and  species," 
in  which  the  former  includes  the  latter,  and  the 
other  is  the  "genus  and  differentia,"  in  which  the 
former  excludes  the  latter.  In  the  comparison  of 
genus  with  species,  genus  denotes  the  class  with 
a,  larger  number  of  individuals  than  the  species, 
and  represents  the  extension  of  a  concept.  In  the 
comparison  of  genus  and  differentia,  genus  denotes 
the  common  qualities  of  the  class  which  are  dis- 
tinct from  the  differences  between  the  individuals 
in  it.  This  equivocal  use  of  the  term  can  be  pre- 
vented by  limiting  the  word  genus  to  the  exten- 
sion of  the  class,  and  conferentia  to  the  intension 
or  common  qualities. 

2.  Differentia. — Differentia,  or  difference,  is  the 
name  for  the  property  or  properties  which  dis- 
tinguish one  species  from  another,  or,  if  we  like, 
the  species  from  the  genus.  Thus  two-footedness 
or  bipedality  is  the  quality  which  distinguishes 
man  from  the  quadrupeds.  Or  better,  the  form  of 
the  leaves  is  a  differentia  of  the  oak  compared 
with  the  ash  tree  ;  the  black  skin  the  difference 
between  the  negro  and  the  Caucasian  ;  mathema- 
tical formula  and  purposes,  the  differentia  of  al- 
gebra compared  with  poetry,  etc.  Whatever  dis- 
tinguishes one  object  from  another  can  be  called 
the  differentia.  It  is  some  characteristic  in  addi- 
tion to  the  common  qualities  and  determines  the 
species  or  individual  under  the  genus. 


4o  LOGIC   AND    ARGUMENT 

3.  Relation  between  Conferentia  and  Differentia. — 
The  first  thing  to  be  remarked  about  the  proper- 
ties expressed  by  these  terms  is  that  the  distinction 
between  them  cannot  be  drawn  in  Singular  terms. 
They  apply  only  to  General  terms  which  comprise 
either  more  than  one  species  or  more  than  one  in- 
dividual. In  an  individual  or  singular  concept 
the  properties  are  all  on  the  same  level.  Only  in 
general  terms  compared  with  the  species  under 
them  can  we  observe  the  distinction  between  con- 
ferentia and  differentia. 

The  second  fact  to  be  observed  is  that  confer- 
entia and  differentia  always  exclude  each  other. 
The  conferentia  is  never  a  differentia,  and  the 
differentia  is  never  a  conferentia  in  the  same  re- 
lation. Thus  feathers  are  a  differentia  between 
birds  and  horses,  and  never  a  conferentia  of  these 
two  species.  Otherwise  they  would  have  the  same 
name  to  denote  them. 

But  the  third  fact  is  that,  although  they  never 
represent  the  same  property  in  the  genus  and 
species,  they  may  still  refer  to  the  same  property 
in  a  class,  provided  that  we  consider  the  different 
relation  in  which  it  may  be  viewed.  Thus  the 
property  which  expresses  the  difference  between 
one  species  and  another  may  itself  be  common  to 
all  the  members  of  the  species  in  which  it  is  found. 
Thus  "two-footedness  "  may  be  the  differentia  of 
man  as  a  species  compared  with  the  horse,  but  the 
conferentia  of  men  as  a  genus  compared  with  "  Cau- 
casian : "  black  skin  is  the  difference  between  the 
"  negro  and  the  Caucasian,"  but  the  conferentia  of 
the  negro  race.  Consequently  conferentia  and 


THE    CONTENT    OK    TERMS  41 

differentia  are  relative  terms.  They  are  names 
for  the  difference  between  the  properties  that  de- 
termine a  concept  as  a  genus  and  those  that  de- 
termine it  as  a  species. 

4.  Essentia  and  Accidentia. — Essentia  and  Acci- 
dentia  are  technical  terms  for  Essence  and  Ac- 
cident, or  essential  and  accidental  properties  re- 
spectively. "  Essential  "  has  generally  been  used 
to  denote  the  same  as  the  common  properties,  or 
what  I  have  called  the  conferentia,  but  "  acciden- 
tal "  has  never  been  used  to  denote  the  differen- 
tia. Hence  the  difference  between  essence  and 
accidents  has  not  meant  the  same  as  the  difference 
between  the  conferentia  and  the  differentia.  Es- 
sence or  essential  has  been  equivocal,  now  denot- 
ing the  conferential  as  distinct  from  the  differen- 
tial, and  again  the  essential  or  more  permanent  as 
distinct  from  the  accidental,  casual  or  variable. 
But  as  the  distinction  between  the  permanent  and 
the  variable  does  not  necessarily  coincide  with 
the  universal  and  the  particular,  or  the  common 
and  the  different,  it  will  be  best  to  use  conferentia 
for  what  is  actually  universal,  whether  it  be  essen- 
tial or  accidental,  and  limit  the  essential  to  those 
properties  which  the  mind  selects  as  the  more  im- 
portant qualities  of  the  subject.  This  will  enable 
us  to  divide  both  the  conferentia  and  differentia 
into  the  essential  and  the  accidental.  Thus  the 
essence  or  essentia  will  denote  not  only  what  is 
common  to  the  class,  but  also  in  addition  those 
common  properties  which  are  necessary  to  the 
subject  or  class,  while  there  may  be  properties 
that  are  common  or  universal,  but  not  necessary 


42  LOGIC   AND    ARGUMENT 

to  the  class  and  hence  called  casual  or  accidental. 
For  instance,  risibility,  or  concha-shaped  ears,  or 
the  comparative  shortness  of  the  little  finger  may 
be  universal  or  conferential  characteristics  of 
man,  and  yet  not  essential  to  him.  The  concept 
man  might  be  retained  though  he  lost  his  risibil- 
ity, the  present  shape  of  his  ears,  or  the  shortness 
of  the  little  finger.  Accidental  properties  are, 
therefore,  those  which  are  treated  as  non-essential 
to  the  subject  of  them  and  are  divided  by  logicians 
into  the  universal  and  the  casual,  which  is  a  recog- 
nition that  the  distinction  between  essence  and 
accident  does  not  coincide  with  that  between  con- 
ferentia and  differentia.  The  distinction,  how- 
ever, between  essence  and  accident  is  not  so  nec- 
essary for  logic  as  is  that  between  conferentia  and 
differentia.  The  latter  is  the  true  basis  for  all 
classifications  and  divisions,  while  that  between 
essence  and  accident  has  probably  only  an  ethical 
value.  But  the  relation  between  the  two  pairs 
of  contrast  is  illustrated  in  the  tabular  outline  of 
properties  in  extension  and  intension,  in  which 
essentia  and  accidentia  are  found  as  divisions  of 
both  conferentia  and  differentia.  The  nature  and 
functions  of  the  latter  and  their  relation  to  the 
determination  of  the  genus  and  species  are  repre- 
sented in  the  following  summarized  outline. 

In  this  table  the  letters  of  the  alphabet  repre- 
sent the  qualities  that  make  up  the  individuals,  as 
A  B  C  D  are  the  qualities  constituting  "  Socrates," 
etc.  But  ABC  are  common  or  conferential  to 
"  Socrates  "  and  "  Solon,"  A  B  F  to  "Pitt"  and 
"  Porson,"  while  D  is  the  differentia  of  "  Socrates  " 


THE    CONTENT    OF    TERMS 


43 


compared  with  the  others,  E  of  "Solon,"  etc. 
ABC  being  common  to  "  Socrates  "  and  "  Solon," 
may  be  treated  as  the  qualities  for  which  the  term 
"  Greek  "  may  stand,  while  A  B  F  being  cemmon  or 
conferential  to  "  Pitt "  and  "  Porson"  may  be  repre- 
sented by  the  term  "  English."  But  here  C  is  the 
differentia  of  "  Greek  "  as  compared  with  "  Eng- 
lish," while  A  B  is  common  or  conferential  to  both, 
and  may  be  represented  by  "  man."  We  have 
then  in  the  scheme  an  illustration  of  the  relation 
both  of  genus  to  species  and  conferentia  to  differ- 
entia, as  well  as  the  relation  of  the  two  pairs  of 
distinction  to  each  other.  Conferentia  and  dif- 
ferentia become  the  names  of  the  q'ualities  by 
which  we  form  the  genus  and  the  species. 


Man . . 


Greek. . .  « 


Socrates . 


Solon . 


English.. 


Porson . 


3d.  Relation  between  Extension  and  Intension. 

Extension  we  have  tound  to  denote  the  number, 


44  LOGIC   AND    ARGUMENT 

though  indefinite,  of  the  objects  denoted  by  a 
term,  and  intension  the  qualities  expressed  or  im- 
plied by  it.  We  find  also  that  every  term  has  the 
property  both  of  extension  and  intension.  Now 
the  intension  always  represents  a  certain  quantity 
of  attributes,  so  that  we  are  enabled  to  express 
a  relation  between  the  quantity  of  extension  and 
the  quantity  of  intension  expressed  by  a  term  ; 
that  is,  the  number  of  objects  denoted  by  it  and 
the  number  of  qualities,  though  only  in  relation  to 
a  wider  genus  or  a  narrower  species.  Thus  "  tree  " 
includes  mathematically  (extensively)  all  the  in- 
dividuals under  "  oak,"  "  elm,"  "  ash,"  "  pine,"  etc., 
and  also  denotes  the  conferentia  or  common  qual- 
ities of  all  these  individuals.  But  "  oak  "  repre- 
sents a  smaller  number  of  individuals  than  "  tree," 
while  it  also  denotes  a  larger  number  of  properties, 
at  least  one  property  more  than  "  tree."  Hence 
its  intension  is  larger  than  tree,  while  its  exten- 
sion is  smaller.  A  similar  illustration  can  be  found 
in  comparing  any  genus  and  species  :  as  "  quad- 
ruped "  and  "  horse."  "  Quadruped  "  denotes  more 
individuals  than  horse,  but  fewer  qualities.  It 
can  stand  only  for  the  conferentia  of  all  four- 
footed  animals,  possibly  only  one  property,  and 
does  not  indicate  the  differentia.  The  species 
"horse"  in  this  case  contains  all  the  conferentia 
of  "quadruped,"  and  something  more,  the  differ- 
entia ;  but  it  denotes  fewer  individuals.  Hence 
we  can  say  that  the  extension  of  "  quadruped  "  is 
greater,  and  that  of  "  horse  "  is  less,  while  the  inten- 
sion of  "  quadruped  "  is  less  and  that  of  "  horse  " 
is  greater.  The  result  of  this  is  that  we  can 


THE    CONTENT   OF   TERMS  45 

formulate  this  relation  in  a  law.  It  is  that  the  ex- 
tension increases  as  the  intension  decreases,  and  vice 
versa,  or  extension  and  intension  vary  in  an  inverse 
ratio  to  each  other.  We  may  symbolize  this  rela- 
tion by  a  diagram  as  follows  : 


V    A    7 

wlXy 

Y         Y 

A     EUROPEAN    l\ 

/'   \   '  ~f         \ 

/   -- 


/  MAN  _  \  /  PLATO  \ 


Extension.  Intension.  Extension  and  Intension. 

FIG.   I.  FIG.  II.  FIG.   III. 

In  Fig.  I.  the  base  of  the  pyramid  represents  the 
largest  extension,  which  decreases  until  it  reaches 
its  minimum  in  "  Plato."  Fig.  II.  reverses  the 
order  of  terms,  but  still  uses  the  base  of  the  pyra- 
mid to  represent  the  largest  quantity,  in  this  case 
of  intension,  which  decreases  until  it  reaches  its 
relative  minimum  in  the  term  "  man."  Fig.  III. 
shows  the  inverse  ratio  of  both  properties,  the 
bases  and  apices  being  arranged  to  suit  this 
fact. 

This  formula  has  its  qualifications.  In  the  first 
place  it  may  apply  only  in  the  majority  of  cases, 
and  it  is  not  a  necessary  law,  except  for  inter- 
mediate classes  between  individuals  and  remoter 
genera.  In  the  second  place,  no  mathematical 
relation  between  extension  and  intension  can  be 
determined  either  absolutely  or  relatively  be- 


46  LOGIC    AND    ARGUMENT 

tween  different  species,  or  different  genera.  The 
law  applies  only  in  the  relation  between  genus 
and  species. 

III.  ANALYSIS  OF  CONCEPTS — This  is  a 
process  of  unfolding  the  meaning  and  implications 
of  terms.  That  is  to  say,  it  involves  the  recogni- 
tion and  statement  of  what  is  found  in  their  quanti- 
tative and  qualitative  import.  We  have  found  that 
the  content  of  terms  consists  in  the  particular  ideas 
they  express,  and  these  ideas  are  their  capacity  to 
denote  number  of  some  kind  and  their  capacity 
to  denote  properties  of  the  things  named.  Hence 
analysis  is  only  the  conscious  statement  of  all  that 
is  involved  in  their  number  and  property  power. 
There  are  three  forms  of  this  analysis.  They  are 
Definition,  Division,  and  Partition.  Each  of  these 
processes  requires  separate  explanation. 

ist.  Definition. — Definition  is  that  process  of 
analysis  which  states  the  conferentia  and  differentia 
ofa  term  orconcept.  It  is  commonly  called  the  anal- 
ysis of  the  genus  and  differentia,  but  previous  dis- 
cussion shows  why  we  use  the  term  "conferentia" 
instead  of  "genus."  It  is,  of  course,  the  term  for 
the  genus  that  is  named  in  the  definition,  but  it  is 
not  taken  in  its  mathematical  or  extensive,  but 
purely  in  its  intensive  sense  to  denote  the  confer- 
entia or  general  qualities  expressed  by  the  term. 
An  illustration  of  definition  would  be  :  "  A  horse 
is  a  domestic  quadruped,  used  exclusively  for  the 
purpose  of  drawing  vehicles  or  performing  definite 
services  in  the  form  of  work  or  pleasure."  This  is 
necessarily  a  little  indefinite,  but  it  names  the 
genus  "domestic  quadruped"  denoting  the  con- 


THE   CONTENT   OF   TERMS  47 

ferentia,  and  the  specific  qualities  which  may  be 
taken  as  the  differentia.  Taking  "  rational  "  as  a 
differentia,  we  might  define  "  man  "  as  a  "  rational 
animal,"  the  term  "animal  "  referring  to  the  con- 
ferentia. 

The  essential  purpose  of  a  definition  is  to  make 
clear  and  definite  the  meaning  of  a  term  or  con- 
cept, giving  it  limits,  or  circumscribing  the  field 
of  ideas  which  it  represents.  But  the  word  "defi- 
nition "  is  often  taken  in  a  broad  sense  to  denote 
any  method  of  indicating  limits  of  this  kind,  and 
hence  we  may  recognize  three  forms  of  it  in  com- 
mon parlance  :  (a)  Etymological  Definition,  which 
is  nothing  more  than  giving  the  root  derivation  of 
a  term  ;  (b)  Descriptive  Definition,  which  is  any 
statement  of  fact  about  a  term  or  object  not 
equivalent  to  it,  and  is  not  a  true  or  accurate  defi- 
nition of  it,  and  (c)  Logical  Definition,  which  is  the 
proper  meaning  of  the  term  "  Definition"  in  logic. 
The  peculiar  nature  of  this  process  is  that  it 
makes  the  subject  and  predicate  of  the  proposition 
identical,  in  which  the  definition  is  given.  The 
rules  which  regulate  correct  logical  definition  are 
as  follow  : 

1.  A  definition  should  state  the  essential  attri- 
butes of  the  species  defined. 

2.  A  definition  must  not  contain  the  name  or 
word  defined.     Otherwise  the  definition  is  called 
a  circulus  in  definiendo. 

3.  The  definition  must  be  exactly  equivalent  to 
the  species  defined. 

4.  A  definition  should  not  be  expressed  in  ob- 
scure, figurative,  or  ambiguous  language. 


48  LOGIC   AND    ARGUMENT 

5.  A  definition  must  not  be  negative  when  it  can 
be  affirmative. 

2d.  Division. — Division  is  an  analysis  of  the 
extension  of  a  term  or  concept,  or  the  separation  of 
a  genus  into  its  species.  Thus  we  are  said  to 
divide  the  genus  "  tree  "  when  we  name  the  species 
under  it,  as  "oak,"  "elm,"  "ash,"  etc.,  and  these 
again  into  narrower  species.  But  in  determining 
the  nature  of  the  process,  and  in  regulating 
its  correct  form,  three  things  must  be  taken 
into  account :  (i)  The  Principle  of  Division,  (2) 
The  Kinds  of  Division,  and  (3)  The  Rules  for 
Division. 

1.  The  Principle  of  Division. — This  is  called  the 
Fundamentum  Divisionis,  or  principle  which  shall  de- 
termine the  method  of  legitimate  analysis  for  ex- 
tension.    It  asserts  that  every  logical  division  must 
be  carried  out  upon  some  principle  which  will  be 
some  quality  whose  differences  in  kind  may  serve 
for  distinguishing  the  species  under  the  genus. 
Thus  in  dividing  the  genus  "man  "  I  may  take  color 
as  the  principle  of  division,  and  determine   the 
species  by  the    differences  in   kind  of   color,  as 
"white  man,"  "black   man,"  "  red  man,"  etc.,  or 
"  Caucasian,"  "  Negro,"  "  Indian,"  etc.    Or  I  might 
take   language  as   the  principle   of  division,  and 
divide  "man  "  into  "  Aryan,"  "  Semitic,"  "  Turan- 
ian," etc. 

2.  The  Kinds  of  ZVw/V//.— There  are,  of  course, 
forms  of  false  and  forms  of  true  division.     The 
latter  are  the  only  cases  to  which   any  technical 
names  have  been  given.     One  of  the  false  forms  is 
called  Cross  Division.     This  is  the  form  in  which 


THE    CONTENT    OF    TERMS  49 

more  than  one  principle  of  division  has  been  em- 
ployed, so  that  the  species  given  overlap  each 
other.  Thus  a  case  of  "  cross  division  "  would  be 
the  separation  of  "  books  "  into  the  species,  "  dic- 
tionaries" and  "  large  books,"  "  useful  books,"  "old 
books,"  etc.  "  Dictionaries"  and  "large  books"  or 
"useful  books"  overlap.  Each  species  must  exclude 
all  others.  The  forms  of  definition  which  are  tech- 
nically recognized  are  two,  Dichotomy  and  what  I 
shall  call  Polytomy. 

(a)  Dichotomy. — Dichotomy  is  that  form  of  di- 
vision which  separates  a  genus  into  two  species 
with  reference  to  the  presence  or  absence  of  a 
given    quality.     The  two  terms  representing  the 
species  become  thus,  one  of  them  a  positive  and 
the  other  a  negative  term.     This  is  the  simplest 
and  surest  mode  of  making  the  division  exhaust- 
ive.    Thus  we  may  divide  "  animals  "  into  "  ver- 
tebrate "  and  "  invertebrate  "  ;  "  Europeans  "  into 
"  Germans  "  and  "  non-Germans  "  ;  "  cities  "  into 
"  large  "  and  "  not-large  "  (or  perhaps  small)  ;  or 
"  climate  "  into  "  temperate  "  and  "  intemperate." 
This  can  be  carried  on  indefinitely  with  either  term 
of  the  dichotomy. 

(b)  Polytomy. — Polytomy  or  manifold  division  is 
that  form  of  it  which  separates  the  genus  into 
species  according  to  the  presence  of  positive  qual- 
ities alone.     Several  or  many  species  are  usually 
necessary  to  exhaust  the  genus.     An  illustration 
would    be    the    division    of    "  quadruped "    into 
"  horses,"  "  dogs,"  "  cattle,"  "  sheep,"  etc.,  though 
it  may  not  be  strictly  scientific.     A  more  accurate 
instance  is  the  following  : 

4 


5° 


LOGIC    AND    ARGUMENT 


Figures . . 


Plane. 


Rectilinear 


Curvilinear 


f  Rectilinear 


(  Trilateral. 
<  Quadrilateral. 
(  Multilateral. 

f  Circular. 
I  Elliptic, 
j  Parabolic. 
(_  Hyperbolic. 

I  Tetrahedral. 
•<  Pentahedral, 
f  Sextahedral,  etc. 


Solid. 


f  Spherical. 
I  „       ...  Conical. 

I  Cumlmear-j  Cylindrical. 
Paraboloidal. 


In  this  instance,  we  observe  that  the  principle 
of  division  may  change  for  each  independent 
class,  but  not  for  those  that  stand  as  species 
under  the  same  genus.  Moreover,  in  all  such  di- 
vision the  genus  in  relation  to  the  species  is  said 
to  be  super  or  dinate,  a  species  in  relation  to  a  genus 
is  said  to  be  subordinate,  and  a  species  in  relation 
to  a  species  is  said  to  be  co-ordinate.  Thus  "  Fig- 
ures "  is  superordinate  to  "  Plane,"  "  Plane  "  is 
subordinate  to"  Figures,"  and  "  Plane"  is  co-ordi- 
nate with  "  Solid." 

3.  The  Rules  of  Division. — A  rule  of  division 
represents  the  condition  under  which  the  process 
shall  be  carried  out  and  so  regulates  the  manner 
of  doing  it.  Hamilton  enumerates  seven  rules, 
but  Jevons  reduces  them  to  three,  which  are  all 
that  are  necessary  for  practical  purposes.  They 
are  as  follows  : 

(a)  Every  division  should  be  governed  by  a 
single  division. 


THE    CONTENT    OF   TERMS  51 

(b)  The  constituent  species  should  exhaust  the 
genus. 

(c)  The  co-ordinate  species  should  be  recipro- 
cally exclusive. 

3d.  Partition. — Partition  is  an  analysis  of  the 
intension  of  a  term  or  concept  without  regard  to 
the  relation  between  genus  and  species,  or  that 
between  conferentia  and  differentia.  It  unfolds 
the  qualitative  meaning  of  a  term,  or  separates  a 
whole  into  its  parts.  It  is  simply  a  process  of 
describing  an  object  by  its  qualities  or  the  parts 
constituting  it.  There  are  two  kinds  :  (i)  Mathe- 
matical or  Quantitative  Partition,  and  (2)  Logical 
or  Qualitative  Partition. 

1.  Mathematical   Partition. — Mathematical  par- 
tition  is  the  analysis  of  a  whole  into  its  parts  as 
expressed  in  terms  of  space  or  time.     This  means 
that  it  looks  at  things  as  space  or  time  wholes. 
Thus  "  house,"  "  tree,"    "  Germany,"    are    space 
Wholes,  as  being  objects  which  occupy  space,  and 
"  age,"   "  life"  (in   one  of  its  senses),  "  the  civil 
war,"  etc.,  are  time  wholes.     Mathematical  parti- 
tion when   applied  to  them  divides  them  into  the 
separate    parts    which     make   the    whole.      Thus 
"  tree  "  would  be  mathematically  partitioned  into 
"roots,"    "trunk,"    "branches,"   and    "leaves;" 
"house,"     into     "walls,"    "doors,"    "windows," 
"rooms,"    "roof,"   etc.;    "age,"    into   "infancy," 
"  childhood,"  "  maturity,"  "  old  age,"  etc.      No  re- 
gard here  is  paid  to  genus  and  species. 

2.  Logical  Partition.  —  Logical  partition  is  the 
analysis  of  a  whole   into  its   properties,  relations, 
etc.     Thus  "  tree  "  would  be  logically  partitioned 


«J2  LOGIC    AND    ARGUMENT 

into  "  color,"  "  hardness,"  "  shape,"  "  growth," 
"  utility,"  etc.,  or,  to  put  it  more  systematically, 
into  material  and  economic  qualities  with  their 
subdivisions.  "Man"  may  be  partitioned  into 
animal  and  rational  properties  each  with  their 
subdivisions.  There  is  here  no  reference  to  genus 
and  species,  except  as  classification  of  the  prop- 
erties is  involved.  This  process  furnishes  the 
aspects  in  which  a  concept  may  be  viewed,  and 
enables  us  to  examine  the  whole  content  of  an 
idea,  concept,  or  object  without  distinction  of 
attributes,  though  they  may  be  systematically 
viewed  at  the  same  time. 

3.  Rules  of  Partition,  —  Partition  is  sometimes 
considered  as  a  kind  of  Division,  and  is  treated 
as  that  form  of  it  which  separates  a  whole  into  its 
component  attributes  instead  of  its  component 
species.  This  is  a  legitimate  view  of  it,  though  it 
is  treated  co-ordinately  with  division  here  in  order 
to  emphasize  the  use  of  it  for  the  purpose  of  fur- 
nishing the  distinct  aspects  of  a  theme  in  dis- 
course which  are  not  so  easily  illustrated  by 
division  into  species.  The  principles  which  regu- 
late it  are  much  the  same,  though  practical 
purposes  are  served  by  the  mention  of  only  a  few 
of  the  more  important  ones. 

(a)  The  analysis  of  the  intension   should  be  ex- 
haustive. 

(b)  The  properties  considered  should  be  classi- 
fied and  distinguished  according  to  the  principles 
of  division. 


EXPLANATORY   DISCOURSE 

I.  INTRODUCTION — We  have  found  what  the 
logical  processes  are  which  represent  the  analysis 
of  a  conception  or  theme  into  its  parts  or  meaning, 
and  we  have  now  to  examine  the  application  of 
them  to  discourse  and  more  especially  to  outline 
the  principles  which  regulate  the  constructive 
processes  of  thought  expression.  All  discourse, 
whether  literary  or  explanatory  or  both  combined, 
is  most  satisfactory  to  the  mind  when  it  is  syste- 
matic and  orderly.  The  impression  produced 
upon  the  mind  by  such  discourse  is  more  distinct 
when  it  follows  definite  principles  and  purposes. 
Its  efficiency  in  both  the  aesthetic  and  the  logical 
field  is  greatest  when  it  is  systematic.  The  ex- 
planatory stage,  however,  is  but  the  preliminary 
step  toward  confirmation,  which  will  have  to  be 
discussed  somewhat  later.  But  at  present  we 
have  to  examine  how  the  expression  of  ideas  with- 
out proof  can  be  systematized,  and  to  show  what 
methods  are  necessary  to  that  end. 

There  are  two  general  processes  involved  in 
explanation.  They  are  Analysis  and  Synthesis,  as  I 
have  named  them.  Less  technically,  the  two  proc- 
esses may  be  called  the  discovery  of  the  parts  of 
53 


54 


LOGIC    AND    ARGUMENT 


a  complex  idea,  and  the  arrangement  of  them  to 
give  a  clear  conception  of  them  as  wholes. 
5  II.  ANALYSIS  OF  THEMES.— The  analysis 
of  a  conception  or  theme  must  precede  and  con- 
dition the  orderly  synthesis  or  composition  of  ma- 
terials to  make  complete  discourse.  It  consists 
of  the  several  processes  of  Definition,  Division, 
and  Partition.  But  these  must  be  applied,  not  for 
their  own  account,  but  with  reference  to  some 
other  end  than  themselves.  Hence  the  special 
way  of  treating  any  given  theme,  in  so  far  as  these 
processes  are  concerned,  will  vary  with  the  sub- 
ject-matter and  its  complexity.  But  nevertheless 
some  general  rules  and  conceptions  can  be  fol- 
lowed in  all  cases. 

The  analysis  of  a  theme  is  simply  the  selection 
of  all  the  parts,  incidents,  attributes,  relations,  and 
classes  expressed  by  it.  The  great  object  of  the 
process  is  to  indicate  the  compass  of  the  subject 
and  to  determine  the  right  order  of  procedure  in 
dealing  with  it.  It  may  be  briefly  defined  as  the 
process  of  skeletonizing  a  subject.  This  is  a  process 
of  mapping  out  the  divisions  and  topics  calculated 
to  give  a  clear  and  exhaustive  treatment  of  a 
theme.  The  order  of  procedure  must  be  that  of 
Definition,  Division,  and  Partition.  The  functions 
served  by  all  three  of  these  methods  are  those  of 
indicating  clearly  the  limitations  under  which  the 
explanation  is  to  be  taken.  They  bring  thought 
and  expression  down  to  definite  and  circumscribed 
limits.  The  manner  in  which  such  a  skeleton  is 
to  be  used  will  depend  upon  the  tastes  and  object 
of  the  writer.  First  it  may  be  used  merely  to  pre- 


EXPLANATORY    DISCOURSE  55 

pare  the  order  of  treatment  to  be  given  a  theme, 
without  being  embodied  as  a  skeleton  in  the  body 
of  the  discourse.  Second,  it  may  be  incorporated 
with  the  introduction  as  an  index  to  the  reader  of 
what  the  logical  conception  of  the  whole  is  to  be. 
The  first  form  leaves  to  the  reader  the  discovery 
of  the  outline.  This  often  has  its  advantages 
where  the  object  is  merely  to  have  system  without 
producing  the  impression  that  the  discussion  is 
for  the  sake  of  the  system  alone.  Third,  the  out- 
line may  be  distributed  throughout  the  treatise  or 
discourse,  especially  where  we  are  dealing  with 
the  student  mind,  partly  for  the  purpose  of  train- 
ing in  habits  of  logical  and  systematic  conception 
and  thinking,  and  partly  to  aid  in  the  clearer  com- 
prehension of  the  subject.  But  in  all  cases  of  ex- 
planatory discourse,  as  here  considered,  whether 
the  outline  be  embodied  in  the  discourse  or  not,  it 
should  have  a  place  in  the  writer's  mind. 

In  suggesting  rules  for  practice,  however,  it  is 
important  to  keep  in  view  the  kind  of  discourse  to 
which  they  are  meant  to  apply.  I  have  intended 
the  process  of  applied  analysis  to  be  limited  to 
what  I  have  called  explanatory  as  distinct  from 
literary  discourse.  Literary  prose  I  have  intended 
to  be  a  sphere  of  expression,  not  designed  to  con- 
vince or  instruct  the  reason  as  its  main  object, 
but,  like  poetry,  to  be  governed  by  (esthetic  rules 
and  ends.  Of  course,  both  poetry  and  literary 
prose  may  combine  logical  with  aesthetic  objects, 
and  when  they  do  must  be  governed  in  the  same 
proportion  by  logical  principles.  But  I  am  here 
laying  down  rules  to  apply  only  to  what  I  have 


tj6  LOGIC   AND   ARGUMENT 

chosen  to  call  explanatory  discourse,  which  has 
for  its  chief  object  to  impart  or  communicate  ideas 
for  the  instruction  of  the  intellect,  and  either  does 
not  consider  aesthetic  taste  at  all  or  makes  this  of 
secondary  importance  so  far  as  that  end  is  con- 
cerned. The  term  explanatory  discourse,  there- 
fore, stands  for  that  form  of  it  which  is  exclusively 
employed  with  logical  processes  and  logical  ob- 
jects. The  rules  for  literary  or  aesthetic  discourse 
may  be  wholly  different.  Of  them  I  do  not  pro- 
pose to  treat.  Outline  and  skeleton  analysis 
may  not  be  necessary  in  aesthetic  literature  pure 
and  simple,  but  only  when  combined  with  the  log- 
ical and  explanatory.  But  for  the  latter  this  proc- 
ess is  essential  for  clearness,  effectiveness,  and 
comprehension,  and  more  especially  for  the  com- 
munication of  systematic  ideas,  which  is  its  object. 
All  rules  of  procedure  here  adopted,  therefore, 
will  leave  the  student  free  to  accept  any  laws  of 
literary  taste  that  aesthetics  require.  We  are  here 
concerned  only  with  that  expression  of  thought 
that  aims  to  reproduce  the  rational  order  which 
the  mind  finds  by  reflection  on  the  world  and  phe- 
nomena. This  order  represents  the  unity  of  log- 
ical relations,  involving  the  proper  selection  of 
ideas,  topics,  and  marshalling  of  material  for  the 
purpose  of  influencing  conviction. 

i  st.  Application   and   Use  of  Definition The 

first  step  in  explanatory  discourse  is  definition. 
The  nature  of  this  process  has  already  been  indi- 
cated and  it  only  remains  to  show  how  it  is  to  be 
used  and  what  its  functions  are  in  systematic 
thought  and  expression. 


EXPLANATORY    DISCOURSE  57 

As  explanation  is  the  systematic  arrangement 
of  the  facts  involved  in  a  theme,  the  first  duty  on 
the  part  of  a  writer  is  to  define  his  subject.  The 
definition  must  include  a  clear  idea  of  the  term  or 
terms  in  the  theme,  and  of  the  proposition  when 
the  theme  is  so  comprehensive.  Thus  if  the  sub- 
ject of  a  descriptive  discourse  is  "  Houses,"  the 
first  thing  to  do  will  be  to  define  the  general 
term  "  house."  The  definition  may  be  made  to 
include  the  historical  and  etymological  meaning 
of  the  term  itself,  but  should  terminate  in  the 
logical  statement  of  the  conferentia  and  differen- 
tia denoted  by  it  in  order  that  it  may  not  want  in 
clearness.  If  the  theme  be  a  proposition,  both 
terms  or  all  terms  in  it  may  be  subjected  to  the 
same  process,  and  the  meaning  of  the  proposition 
of  the  whole  determined.  So  much  for  the  first 
step. 

The  function  of  definition  is  to  give  limitations 
to  the  discourse  and  to  aid  the  comprehension  of 
those  for  whom  the  communication  of  ideas  is  in- 
tended. It  brings  to  specific  notice  the  proper- 
ties expressed  by  a  term,  and  makes  clear  the 
most  essential  qualities  involved  in  its  meaning. 
It  thus  conveys  an  idea,  definite  and  clear,  to  the 
person  receiving  the  information  communicated, 
and  more  especially  indicates  the  facts,  things,  or 
qualities  not  to  be  considered  in  the  use  of  the 
term.  This  latter  function  is  what  is  meant  by 
giving  an  idea  or  term  limitations.  Apart  from 
definition  it  might  mean  anything.  But  this  proc- 
ess shuts  out,  at  least  by  implication,  all  that  the 
thing  is  not,  and  also  distinguishes,  in  what  it  is, 


58  LOGIC   AND    ARGUMENT 

between  the  essential  and  the  unessential  marks 
constituting  an  object.  Thus  if  I  am  asked  to 
discourse  upon  the  theme  "  Man,"  my  first  task 
must  be  to  indicate,  at  least  in  the  most  general 
way,  for  what  the  term  man  essentially  stands.  I 
may  say  that  "  Man  is  that  genus  of  organized  be- 
ings which  show  the  attributes  of  rationality," 
etc.,  or  that  he  is  "that  species  of  biped  which 
exhibits  certain  peculiar  mental  and  moral  habits 
of  life,"  etc.  The  distinctive  qualities,  of  course, 
would  have  to  be  named.  But  the  process  would 
bring  out  the  aspects  of  man  and  his  nature  which 
were  to  come  under  consideration  in  the  discourse. 
Besides,  it  decides  the  compass  and  range  of  the 
discussion,  showing  just  what  conception  and 
facts  are  to  be  considered  in  the  theme.  Ideas 
thus  have  definiteness  and  clearness. 

It  is  not  necessary  to  indicate  in  the  outline  of 
a  theme  that  the  process  of  definition  is  going  to 
be  followed.  This  may  be  done  in  text-books  and 
theses  designed  for  a  certain  kind  of  instruction. 
But  the  main  thing  in  all  cases  is  the  application 
of  the  process  as  the  necessary  means  of  orienta- 
tion in  a  subject ;  that  is,  the  necessary  means  of 
making  clear  the  general  nature  and  scope  of  the 
subject.  It  may  be  applied  at  every  step  in  the 
development  of  a  theme. 

2d.  The   Application   and  Use  of  Division 

Division  was  found  to  be  the  analysis  of  a  con- 
ception or  theme  into  its  species  or  kinds,  as 
"  man,"  into  Caucasian,  Negro,  Malay,  etc.  In 
discourse  this  process  is  to  be  applied  to  the  de- 
termination of  the  general  parts  of  the  subject, 


EXPLANATORY    DISCOURSE  59 

though  in  certain  kinds  of  discourse  Partition  will 
take  its  place.  But  in  most,  if  not  all,  themes  it 
will  have  a  function  to  perform.  Thus  if  the  sub- 
ject be  "Books,"  the  mode  of  division  for  the  dis- 
course will  depend  upon  the  aspect  of  the  subject 
to  be  considered,  and  the  topics  for  chapters  or 
sections  selected  accordingly.  If  "books"  are 
to  be  discussed  from  the  point  of  view  of  their 
subject-matter,  they  might  be  divided  into  philo- 
sophic, scientific,  literary,  religious,  etc.,  as  repre- 
senting the  distinct  kinds  to  be  treated  separately. 
If  the  theme  is  to  be  considered  in  respect  of  their 
form, the  division  might  be  folios,  quartos,  octavos, 
duodecimos,  etc.  If  the  question  concerns  their 
relation  to  civilization  the  divisions  might  be  scien- 
tific books,  political  books,  artistic  books,  religious 
books,  etc.  In  all,  they  are  classified  and  discussed 
with  reference  to  some  principle  of  division  that 
determines  the  point  of  view  to  be  considered.  If 
again,  for  instance,  the  theme  be  "  Protection," 
we  could  divide  it  into  chapters  on  Protection  of 
Manufacturers,  Protection  of  Agriculture,  Protec- 
tion of  Trade,  Protection  of  Labor,  etc.  Or  in 
another  form,  if  the  question  is  as  to  methods,  it 
can  be  divided  into  Revenue  Protection,  Bounty 
Protection,  Prohibition  of  Imports,  etc.  In  all 
these  cases  separate  applications  of  the  main  prin- 
ciple are  concerned  and  require  separate  treat- 
ment. 

The  chief  function  of  division  is  to  reserve  for 
distinct  discussion  those  special  aspects  of  a  sub- 
ject which  are  not  immediately  recognizable  in 
the  general  definition,  but  are  found  in  the  differ- 


60  LOGIC   AND    ARGUMENT 

ences  that  mark  the  species.  Definition  states 
what  characterizes  the  whole  class  without  regard 
to  species,  and  so  deals  with  the  essential  inten- 
sion of  a  conception.  Division,  on  the  other 
hand,  dealing  with  the  extension,  recognizes  the 
differences  characterizing  the  species  under  the 
genus.  Thus,  in  the  subject  of  protection,  the  form 
of  it  denoted  by  bounties  involves  certain  inci 
dents  and  influences  not  noticeable  in  its  appli- 
cation in  revenues.  Hence  the  reservation  of  this 
form  of  it  for  separate  treatment  offers  an  oppor- 
tunity to  discuss  this  aspect  of  it  wholly  distinct 
from  the  incidents  common  to  every  kind  of  pro- 
tection. 

3d.  The  Application  and  Use  of  Partition. — 
The  chief  function  of  Partition  is  the  presentation 
of  the  aspects  of  a  theme.  As  already  shown,  it 
is  the  division  of  a  concept  into  its  attributes, 
implications,  and  relations,  and  so  the  analysis 
of  its  intension.  This  is  only  an  application  of 
the  principles  of  division  to  the  properties  and 
relations  of  a  thing  instead  of  its  species,  and  af- 
fords an  opportunity  to  systematize  discourse  in 
regard  to  the  implications  of  a  theme.  Certain  in- 
cidents can  be  made  to  centre  about  a  given  attri- 
bute or  relation  that  might  otherwise  be  scattered 
about  through  the  discussion  without  relevancy  or 
proper  order.  Partition  thus  presents  a  system  of 
topics  distinct  from  species  as  centres  of  gravitation 
for  relevant  matters  of  interest  to  that  aspect. 
Thus  if  the  theme  be  "  House,"  I  may  partition  it 
into  origin,  style,  utility,  etc.,  or  foundation,  walls, 
floors,  windows,  etc.,  and  discuss  the  appropriate 


EXPLANATORY    DISCOURSE  6 1 

incidents  connected  with  each  aspect.  Or  again, 
if  the  theme  be  "  Protection,"  it  may  be  partitioned 
into  history,  administration,  effects,  etc.,  or  mo- 
tives, application,  results,  etc.  "  Books  "  might  be 
partitioned  into  such  topics  as  form,  size,  style  of 
print,  binding,  cost,  utility,  etc.  Each  topic  can  be 
made  the  subject  of  a  section  or  chapter,  accord- 
ing to  the  purpose  of  the  writer. 

4th.  Methods  of  Applying  Analysis — The  one 
great  object  of  analysis  is  clearness  and  system- 
atization  of  thought  and  discourse.  But  it  can  be 
carried  out  in  a  way  to  make  discourse  too  mechan- 
ical and  to  bury  the  thought  in  a  mass  of  outline. 
A  proper  mean  should  be  used  in  the  process. 
There  are  three  ways  in  which  topical  analysis  can 
be  applied:  (i)  We  may  outline  the  whole  subject 
in  the  introduction  and  omit  farther  express  anal- 
ysis from  the  body  of  the  discourse,  using  only  so 
much  as  is  necessary  for  the  chaptering.  This  will 
avoid  all  mechanical  appearances  in  the  discussion. 

(2)  We  may  distribute  the  outline  throughout  the 
discourse    so  that  each  chapter  and   section  will 
represent  a  distinct  recognition  of   the  separate 
topics  treated.     Whether  mechanical  or  not,  this 
will  be  necessary  for  certain  kinds  of  discourse. 

(3)  We  may  make  the  analysis  of  a  theme  and  fol- 
low it  without  any  explicit  recognition  of  it  in  a 
mechanical  form,  but  leaving  it  to  be  discovered 
by  the  reader,  if  necessary.     This  last  method  ob- 
tains the  advantages  of  systematization  and  logical 
discourse  without  its  mechanical  features. 

The  method  of  applying  the  analysis  will  not 
always  be  the  same.  (i)  It  may  sometimes  be 


62  LOGIC    AND    ARGUMENT 

Division  alone  and  (2)  sometimes  Partition  alone. 
At  others,  and  perhaps  In  most  cases,  it  will  be  best 
to  apply  both  Division'and  Partition  together  in 
forming  the  outline.  These  may  be  combined  in 
various  ways.  Division  may  determine  the  topics 
for  the  main  parts  of  the  discourse,  and  Partition 
the  topics  for  the  subordinate  parts.  Sometimes 
even  both  may  be  combined  in  the  main  divisions, 
according  to  the  degree  of  importance  attaching 
to  the  topics  so  arranged.  This  procedure  may 
violate  mechanical  correctness,  but  economy  of 
analysis  may,  at  times,  justify  such  a  departure 
from  mechanical  and  logical  accuracy.  But  gen- 
erally Partition  can  be  applied  to  determine  the 
topics  and  subdivisions  of  the  subordinate  divi- 
sions of  discourse,  as  well  as  often  determining 
those  of  the  main  parts. 

III.  SYNTHESIS  OR  COMPOSITION.  — Syn- 
thesis or  Composition  is  the  arrangement  of  the 
matter  of  thought  about  the  topics  which  analysis 
presents.  It  requires  Proof  or  Confirmation  for 
the  completion  of  the  process.  But  this  part  of  it 
cannot  come  under  consideration  at  present,  nor 
until  we  have  studied  the  nature  of  reasoning. 
Only  so  much  of  the  process  can  be  explained  here 
as  concerns  the  arrangement  of  ideas  to  present  a 
clear  idea  of  the  object  or  theme  which  is  the  sub- 
ject of  discourse.  The  topics  are  mere  centres  of 
gravity  for  the  complex  matters  of  thought  and  so 
afford  a  principle  of  cohesion  for  them,  and  compo- 
sition is  a  process  of  selecting  and  arranging  the 
particulars  of  knowledge  about  their  appropriate 
topics  or  centres  of  gravity.  We  may  divide  it,  for 


EXPLANATORY    DISCOURSE  63 

convenience,  into  three  kinds  :  (i)  Description, 
(2)  Narration,  and  (3)  Exposition.  Description 
applies,  in  the  technical  meaning  given  it  here,  to 
space  wholes  ;  Narration,  to  time  wholes  ;  and  Ex- 
position, to  thought  wholes. 

It  is  important  to  remark  that  there  is  no  essen- 
tial difference  between  the  processes  of  descrip- 
tion, narration,  and  exposition.  The  same  general 
laws  govern  all  of  them.  The  differences  con- 
nected with  them  are  in  the  objects  or  themes 
considered,  and  different  terms  are  applied  to  the 
discourse  in  order  to  recognize  the  differences  in 
the  subordinate  features  of  it.  Certain  subsidiary 
rules  apply  to  discourse  on  space  wholes  that  do 
not  apply  to  time  and  thought  wholes,  as  they  are 
here  called.  The  same  is  true  of  either  of  the 
latter  compared  with  the  others.  But  the  general 
process  of  arranging  materials  is  the  same  in  all 
of  them,  and  gives  rise  to  the  same  laws  of  pro- 
cedure. 

i  st.  Laws  of  Composition  or  Synthesis — A 
law  of  Composition  is  a  rule  regulating  the  process 
of  explanatory  discourse  so  that  it  will  exhibit 
the  greatest  possible  clearness  and  systematiza- 
tion.  It  is  simply  a  condition  of  right  procedure, 
and  affords  a  criterion  for  determining  the  merits 
of  the  discourse.  Such  a  law  represents  some  idea 
according  to  which  the  selection  and  arrangement 
of  material  have  to  be  made. 

i.  Law  of  Selection. — The  law  of  selection  is 
that  condition  which  requires  us  to  distinguish  be- 
tween the  matter  that  is  relevant  and  that  which 
is  irrelevant  to  the  theme  or  any  part  of  the  theme 


64  LOGIC   AND    ARGUMENT 

which  is  under  consideration.     It  is  not  all  of  our 
ideas  about  a  given  subject  that  can  receive  equal 
attention  or  be  used  with   equal  freedom.     The 
selection  of  ideas  and  matter  of  thought  pertain- 
ing to  a  subject  should  be  directed  with  reference 
to  the  manner  in  which  the  theme  is   analyzed. 
Much  can  be  neglected  altogether,  unless  the  pur- 
pose be  to  deal  with  every  aspect  of  the  subject, 
and  even  then   selection  must  be  made  to  distin- 
guish between  what  pertains  to  one  part  and  what 
pertains    to    another.     Thus    if    the    theme    be 
"  House,"  I  should   select  the  things   to  be  said 
about  it  with  reference  first  to  the  definition  of  it, 
and  second  with  reference  to  each  aspect  of  the 
general  theme  chosen  for  separate  treatment.     If 
I  treat  the  subject  as  denoting  some  form  of  resi- 
dence, I  should  exclude  all  matters  pertaining  to 
houses  for  business,  names  of  dynasties,  or  bodies 
of  legislators.     I  should  select  only  matter  bear- 
ing upon  or  included  within  the  notion   of  resi- 
dences.   Or  if  the  theme  be  "The  Moral  Influence 
of  Art,"  I  should  exclude  all  matter  dealing  with 
mere  history  of  art.     In  fact,  its  history  in  every 
aspect  might  be  ignored,  unless  features  of  it  could 
be  given  relevance  to  its  moral  character.     Simi- 
larly all  discussion   of  execution,  finish,  and  style 
could  be  and  ought  to  be  disregarded,  and  only 
the  ideas  and   their  embodiment  and  suggestion 
selected  for  deve-loping  the  theme.     Relevancy  is 
the  distinctive  criterion  of  the  process. 

2.  The  Law  of  Unity. — The  law  of  unity  is  that 
condition  of  explanatory  discourse  which  regulates 
the  arrangement  of  material  after  it  is  selected. 


EXPLANATORY    DISCOURSE  65 

Selection  determines  what  is  relevant  to  the  gen- 
eral theme.  The  law  of  unity  determines  the 
arrangement  of  this  matter  in  its  proper  relation 
to  the  subordinate  topics,  so  as  to  give  system  to 
the  whole.  Besides,  it  is  constructive  in  its  ar- 
rangement, while  selection  only  prepares  the  way 
to  this  unity.  Relevancy  is  also  a  principle  here, 
though  it  is  constructive  as  well  as  selective.  The 
order  of  arrangement  for  producing  unity  will  vary 
with  circumstances.  Now  it  may  take  one  order 
and  now  another,  depending  upon  the  occasion, 
the  object,  the  state  of  public  opinion,  and  what- 
ever is  required  to  make  the  discourse  effective. 
Sometimes  I  may  put  the  most  important  matter 
first,  and  sometimes  the  less  important,  making 
the  presentation  cumulative  in  its  impressiveness. 
The  discretion  of  the  writer  and  the  nature  of  the 
circumstances  must  regulate  this.  But  always 
relevant  arrangement  must  be  the  rule  of  con- 
struction. Thus,  if  I  am  discussing  the  subject 
of  "  Protection  "  and  the  two  subordinate  topics 
under  it,  revenue  and  bounty  protection,  I  should 
not  arrange  facts  illustrating  one  of  these  topics 
under  the  other,  though  the  facts  under  both  have 
also  a  bearing  upon  the  general  theme.  But  facts 
and  figures  on  bounties  should  be  arranged  to  il- 
lustrate the  influence  of  this  specific  kind  of  pro- 
tection, rather  than  the  general  process.  Nor 
should  I  confuse  with  the  facts  relevant  to  these 
subordinate  topics  facts  that  have  only  a  general 
significance.  Again,  if  I  am  explaining  the  theme 
"  Cities,"  I  should  not  confuse  matter  relevant  to 
special  cities  with  that  which  is  relevant  to  the 
5 


66  LOGIC    AND    ARGUMENT 

general  conception.  Everything  in  its  place  is  as 
good  a  logical  as  it  is  a  domestic  maxim. 

2d.  Forms  of  Composition — These  have  al- 
ready been  named  as  Description,  Narration,  and 
Exposition,  according  as  they  are  occupied  with 
space,  time,  or  thought  wholes  as  themes.  We 
have  also  said  that  essentially  they  are  the  same 
in  method,  and  only  certain  interesting  differences 
in  the  themes  or  objects  of  the  discursive  treat- 
ment can  justify  separate  names  for  them.  The 
general  laws  regulating  them,  as  we  have  said,  are 
the  same.  But  the  distinction  of  themes  requires 
certain  modified  rules  of  some  importance  in  the 
management  of  materials,  and  hence  there  will  be 
some  convenience  in  the  use  of  these  terms  in 
spite  of  essential  identity  in  their  content. 

i.  Description. — Description  is  that  process  or 
form  of  explanation  which  exhibits  the  properties, 
attributes,  and  relations  of  spacial  objects  in  their 
proper  order.  Even  mental  and  related  phenom- 
ena will  not  be  excluded  from  this  definition  in- 
asmuch as  they  may  be  treated  as  concomitant 
properties  of  spacial  wholes.  This  description, 
however,  may  take  two  forms,  according  as  it 
deals  only  with  spacial  relations  or  only  with 
properties  of  a  non-spacial  character.  They  cor- 
respond to  mathematical  and  logical  partition. 
Mathematical  description  exhibits  the  parts  of  a 
whole  not  coinciding  with  each  other.  For  in- 
stance, the  mathematical  description  of  a  "  house  " 
would  take  in  their  proper  order  the  separate  and 
individual  parts  of  the  house,  such  as  foundation, 
walls,  doors,  windows,  roof,  furniture,  etc.,  and 


EXPLANATORY    DISCOURSE  6^ 

exhibit  their  form,  structure,  functions,  etc.  Log- 
ical description,  on  the  other  hand,  will  exhibit 
the  properties  and  functions  of  an  object  which 
may  occupy  the  same  space,  arid  so  are  to  that  ex- 
tent independent  of  that  property.  For  instance, 
the  logical  description  of  a  "house  "will  repre- 
sent its  form,  size,  appearance,  artistic  character, 
cost,  use,  etc.,  without  regard  to  mathematical 
divisions. 

The  methods  of  procedure  or  rules  regulating 
the  process,  in  order  to  meet  the  demands  of  the 
laws  of  unity  and  selection,  are  much  the  same, 
with  slight  variation,  for  both  mathematical  and 
logical  description.  Both  require  that  the  most 
important  parts  or  properties  be  taken  first,  and 
the  subordinate  matters  afterward.  But  in  mathe- 
matical description  no  principle  of  logical  division 
can  be  adopted.  The  properties  and  relations 
named  cannot  be  grouped,  but  must  be  taken,  as 
it  were,  in  a  serial  order.  In  logical  description, 
however,  something  of  classification  can  often,  if 
not  always,  be  adopted,  inasmuch  as  the  proper- 
ties of  a  subject  can,  at  least  generally,  be  classi- 
fied. Thus  in  the  logical  description  of  a  "  house," 
I  should  group  together  all  that  is  to  be  said  in 
regard  to  form  and  color,  as  being  both  of  them 
visual  properties.  If  the  theme  be  "man"  we 
should  group  together  the  physical  qualities  and 
not  confuse  with  them  any  of  the  mental.  Sub- 
groups of  each  of  these  can  also  be  taken  in  order 
to  introduce  further  order  into  the  description. 
This  will  involve  the  simultaneous  application  of 
Division  and  Partition  ;  of  Partition  to  the  sub- 


68  LOGIC    AND    ARGUMENT 

ject  and  of  Division  to  its  properties  as  classified. 
In  many  cases  also  mathematical  and  logical  par- 
tition can  be  applied  at  the  same  time  in  combi- 
nation. Thus  by  first  classifying  the  properties 
of  "  man  "  as  physical  and  mental,  and  if  we  desire 
further  to  subdivide  each  group,  the  physical  into 
form,  size,  functions,  complexion,  etc.,  and  the 
mental  into  intellectual,  emotional,  and  moral,  we 
might  then  apply  mathematical  partition  to  the 
form  and  size,  reserving  any  other  process  for 
functions  and  complexion,  while  logical  partition 
would  apply  to  the  mental  properties.  Clearness 
and  convenience  must  be  the  guides  in  each  step. 
2.  Narration. — Narration  is  that  process  of  ex- 
planation which  presents  a  theme  in  its  time  rela- 
tions, or  which  exhibits  events  in  their  proper 
order.  It  will  be  seen  from  this  definition  that 
the  process  is  essentially  history,  no  matter  what 
the  theme  may  be.  This  may  also  have  two 
kinds  :  mathematical and  logical  Narration.  Mathe- 
matical narration  will  divide  the  whole  into  cer- 
tain periods  marked  by  chronological  divisions  of 
importance,  and  exhibit  all  events  within  them  in 
their  order,  perhaps  with  such  subordinate  chrono- 
logical divisions  as  are  necessary  or  convenient  for 
clearness.  Each  period  forms  a  topic  about  which 
relevant  and  appropriate  events  shall  be  grouped. 
Thus  take  the  theme  "  England."  First  I  may  de- 
cide whether  I  shall  treat  the  theme  geologically 
or  politically,  or  in  any  other  way.  The  time  di- 
visions are  likely  to  be  different  in  each  case. 
Taking  it  politically,  I  select  those  dates  which 
best  represent  the  idea  and  its  development  which 


EXPLANATORY    DISCOURSE  69 

I  am  seeking  to  elucidate.  The  usual  chronologi- 
cal divisions  of  English  history  will  illustrate  this 
process.  Logical  narration  will  divide  a  histori- 
cal theme  and  its  periods  into  the  various  aspects 
which  constitute  them  as  wholes  before  narrating 
the  details.  The  narration  may,  at  least  to  some 
extent,  ignore  chronological  limitations  in  this 
operation,  though  applying  them  to  each  separate 
aspect.  Thus  taking  England  again  and  its  gen- 
eral history  instead  of  presenting  all  forms  of  its 
development  in  their  exact  chronological  position, 
I  can  divide  this  history  for  the  whole  and  each 
period  into  political,  industrial,  religious,  scientific, 
aesthetic,  and  moral  aspects,  and  narrate  within 
these  limits  the  facts  and  events  appropriate  to 
each  topic.  This  will  give  the  best  logical  form 
and  order  to  the  discourse,  though  there  may  be 
other  reasons  at  times  for  a  chronological  order 
without  these  divisions.  In  pure  mathematical 
narration  the  principle  must  be  chronological 
order.  In  pure  logical  narration  the  principle 
must  be  logical  classification  and  connection  of 
events  without  regard  to  other  events  in  the  same 
time.  In  many  instances,  however,  it  is  possible 
and  will  be  proper  and  important  to  combine  both 
processes.  This  may  be  done  in  various  degrees 
according  as  the  object  of  the  narration  permits 
it. 

3.  Exposition. — Exposition  is  that  process  of  ex- 
planation  which  exhibits  a  theme  as  a  logical  or 
thought  whole  independent  of  time  or  space  re- 
lations. It  is  a  process  that  deals  largely,  if  not 
wholly,  with  abstract  and  general  conceptions, 


7o 


LOGIC    AND    ARGUMENT 


while  pure  Description  and  Narration  will  be  oc- 
cupied with  concrete  things,  and  will  consider  in- 
dividual objects  and  their  qualities  without  distinc- 
tion between  the  essential  and  accidental.  But 
Exposition  when  dealing  with  thought  wholes 
must  limit  its  process  to  the  essential  properties 
or  events  brought  together.  Every  general  term 
or  concept  can  be  brought  under  this  process, 
which  will  be  a  presentation  of  the  theme  in  re- 
spect of  its  properties  and  related  events  accord- 
ing to  logical  partition  alone.  It  will  therefore 
be  a  process  of  exhibiting  the  nature  of  the  sub- 
ject considered.  The  order  of  selection  will  rep- 
resent the  most  important  properties  or  facts 
concerned,  according  to  the  point  of  view  main- 
tained. The  themes  to  which  Exposition  will  be 
applied  and  to  which  Description  and  Narration 
might  not  require  to  be  applied,  or  might  not  be 
possible,  are  such  as  "science,"  "philosophy," 
"  history,"  "  religion,"  "  politics,"  etc.  Even  more 
concrete  conceptions,  to  which  Description  and 
Narration  might  apply,  can  be  made  the  subject 
of  Exposition,  such  as  "man,"  "quadruped," 
"  forest,"  "  army,"  "  the  age  of  iron,"  "  the  Re- 
naissance," etc.  But  in  its  pure  form  it  limits 
the  process  of  explanation  to  the  properties  and 
events  constituting  an  abstract  whole,  and  con- 
sists in  the  arrangement  of  material  about  topics 
determined  by  the  logical  division  and  partition 
of  the  theme.  Such  conceptions  as  "  govern- 
ment," "poetry,"  "life,"  "virtue,"  are  highly  ab- 
stract, not  because  they  denote  intangible  things, 
but  because  of  their  exceedingly  general  charac- 


EXPLANATORY    DISCOURSE  71 

ter.  But  every  general  term,  taken  as  already  ex- 
plained, may  also  be  an  abstract  or  thought 
whole,  in  that  the  group  of  properties  denoted  by 
it  has  required  intellectual  as  well  as  sensational 
functions  to  produce  them.  Exposition  is  the  pro- 
cess of  unfolding  their  full  content  and  meaning, 
and  demands  the  logical  analysis  of  the  theme  and 
the  arrangement  of  subordinate  matter  in  its  due 
relation  to  the  appropriate  topic. 

IV.  CONCLUSION.— The  only  important  re- 
mark in  the  conclusion  of  this  subject  is  that 
themes  will  often  be  found  capable  of  any  or  all 
three  forms  of  composition.  Some  conceptions 
possess  time,  space,  and  thought  relations,  so  that 
it  is  a  matter  of  convenience  whether  one  or  the 
other  of  the  forms  of  Composition  is  used.  In 
all  of  them  the  essential  step  is  the  analysis,  and 
then  a  perception  of  the  relevancy  of  the  matter 
arranged. 


CHAPTER    V 
PROPOSITIONS 

I.  DEFINITION. — In  the  expression  of  our 
ideas  or  thoughts  we  are  accustomed  to  combine 
terms  and  concepts  in  a  way  to  express  some 
definite  meaning.  Such  a  combination  of  terms 
is  called,  in  common  parlance,  a  proposition,  or 
sentence.  But  for  the  purposes  of  Logic  we  re- 
quire to  be  more  accurate  in  our  account  of  the 
matter.  Hence  a  Proposition  is  any  affirmation  or 
denial  of  an  agreement  between  two  conceptions.  For 
instance,  "Gold  is  a  metal  "is  a  proposition  which 
expresses  an  agreement  or  some  measure  of  iden- 
tity between  "  Gold  "  and  "  metal."  "  Man  is  not 
a  quadruped "  denies  this  agreement.  Every 
proposition  consists  of  two  terms  :  namely,  the 
Subject  and  the  Predicate,  with  a  connecting  ele- 
ment in  the  simplest  form,  which  is  called  the 
Copula.  This  Copula  is  some  form  of  the  verb 
to  be,  with  its  usual  adjuncts.  In  such  propo- 
sitions as  "  Napoleon  ruled  France  "  the  copula  is 
not  expressed,  but  may  be  said  to  be  implied. 
The  verb  and  its  object  constitute  the  predicate, 
and  the  meaning  of  the  proposition  can  be  ex- 
pressed equally  well  in  the  form,  "  Napoleon  was 
the  ruler  of  France."  The  subject  is  that  of 
72 


PROPOSITIONS  73 

which  something  is  affirmed  or  denied.  The 
predicate  is  that  which  is  affirmed  or  denied  of 
the  subject.  The  logical  subject  and  predicate 
may  contain  more  terms  than  would  be  called  by 
these  names  in  Grammar.  They  may  be  repre- 
sented by  any  number  of  terms,  provided  they  con- 
stitute a  single  concept. 

II.  DIVISIONS — Propositions  may  be  divided 
in  a  variety  of  ways,  according  to  the  object  to  be 
served  by  the  division.  In  all  instances,  however, 
Logic  requires  that  the  divisions  mark  a  function 
that  is  represented  in  some  of  the  processes  of 
reasoning.  But  in  regard  to  their  general  import 
I  shall  divide  them  into  Univocal  and  Equivocal 
Propositions.  These  terms  univocal  and  equivocal 
I  shall  give  a  definite  meaning  for  the  purpose. 
They  could  also  be  called  simple  and  ambiguous. 

ist.  Univocal  Propositions. — Univocal  propo- 
sitions are  those  whose  meaning  is  definite  and 
clear,  and  whose  form  of  expression  represents  the 
normal  relation  of  subject  and  predicate,  and  do 
not  imply  complementary  propositions.  They  are 
further  subdivided  into  several  forms. 

i.  Logico- Grammatical  Propositions. — These  are 
propositions  which  have  common  uses  and  names 
in  Grammar  and  Logic.  They  are  sometimes  di- 
vided into  Categorical  and  Conditional,  with  a  sub- 
division of  the  latter  into  Hypothetical  and  Disjunc- 
tive. Sometimes  Conditional  and  Hypothetical 
propositions  are  not  distinguished  at  all,  and  the 
Disjunctive  are  treated  as  a  distinct  class  of  prop- 
ositions by  themselves.  The  latter  division  I 
should  regard  as  the  better,  especially  as  each 


74 


LOGIC    AND    ARGUMENT 


proposition  may  be  said  to  determine  a  form  of 
the  syllogism,  the  Categorical,  Hypothetical  or  Con- 
ditional, and  the  Disjunctive. 

A  Categorical  proposition  is  one  in  which  a  state- 
ment or  assertion  is  made  without  any  qualifying 
conditions.  For  instance,  "  A  is  B,"  or  "  Man  is 
mortal."  The  fact  in  such  cases  is  stated  to  be 
certain  or  known  without  doubt.  It  may  be  only 
an  imaginary  fact  yet,  the  assertion  is  in  the  form 
of  reality. 

A  Hypothetical  or  Conditional  proposition  is 
one  in  which  the  assertion  is  made  to  depend  upon  a 
supposition  of  some  kind  ;  as,  "  If  A  is  B,  C  is  D," 
or  "If  it  rains,  the  ground  will  be  wet."  The  first 
clause  of  the  conditional  proposition  is  called  the 
antecedent,  the  second  is  called  the  consequent. 
The  symbols  of  such  propositions  are  //,  even  if, 
provided  that,  although,  sometimes  when,  and  any 
form  of  expression  denoting  a  condition,  such  as 
had  or  were  introducing  a  proposition  that  is  not 
a  question.  There  are  four  forms  in  which  the 
conditional  proposition  can  be  expressed,  two  of 
which  are  affirmative,  and  two  of  which  are  neg- 
ative. They  are  as  follows  : 

(a)  If  A  is  B,  C  is  D.  (b)  If  A  is  not  B,  C  is  D. 
(c)  If  A  is  B,  C  is  not  D.  (d)  If  A  is  not  B,  C  is 
not  D. 

A  Disjunctive  proposition  is  one  which  implies 
or  asserts  an  alternative  in  the  relation  between 
the  subject  and  predicate  ;  as,  "A  is  either  B  or 
C,"  or  "Metals  are  either  hard  or  soft."  The 
symbols  of  the  disjunctive  proposition  are  either  — 
or.  They  are  its  symbols,  however,  only  when 


PROPOSITIONS 


75 


they  denote  mutual  exclusion  between  the  altera- 
tives, and  not  when  they  denote  merely  the  suffi- 
ciency of  one  or  the  other  of  two  facts  to  account 
for  a  phenomenon  without  excluding  the  exist- 
ence of  the  alternative  circumstance  ;  as,  "  Gib- 
bon was  either  very  industrious  or  very  talented." 
The  disjunction,  however,  when  it  is  complete  and 
formally  correct,  means  that  the  connection  be- 
tween subject  and  predicate  must  be  only  one  or 
the  other  of  two  things.  In  the  proposition  A  is 
either  B  or  C  ;  the  question  whether  A  is  B  or 
whether  A  is  C  is  indefinite  or  undecided,  but  it  is 
definitely  one  or  the  other,  and  hence  the  propo- 
sition means  either  that  A  is  B  and  is  not  C,  or 
that  A  is  not  B  and  is  C,  or  that  A  is  C  and  is  not 
B,  or  finally  that  A  is  not  C  and  is  B.  Hence  it 
means  that  if  A  is  B  it  is  not  C,  etc.  This  is  the 
reason  that  it  is  usually  classed  as  a  conditional 
proposition.  But  if  it  be  closely  examined  it  will 
be  found  to  contain  both  categorical  and  con- 
ditional elements.  It  is  categorical  in  its,  form,  or 
mode  of  expression,  and  conditional  in  its  matter, 
or  meaning.  The  relation  of  form  and  matter  in 
the  three  propositions  may  be  summarized  as  fol- 
lows : 


Proposit 


(  Categorical  =  Assertory  in  form  and  matter, 
itiuns  <  Conditional  =  Hypothetical  in  form  and  matter. 

(.  Disjunctive  ==  Categorical  in  form,  but  conditional  in  matter. 


2.  Logico-Qualitative  Propositions. — Propositions 
may  be  divided  into  Affirmative  and  Negative,  ac- 
cording as  they  affirm  or  deny  the  agreement  be- 
tween subject  and  predicate.  This  relation  is 


called  or  determines  what  is  regarded  as  their 
quality.  An  affirmative  proposition  asserts  an 
agreement  between  subject  and  predicate  ;  as, 
"Gold  is  yellow,"  or,  "  Doves  are  birds."  A  neg- 
ative proposition  is  one  which  denies  an  agreement 
between  subject  and  predicate  ;  as,  "  Men  are  not 
quadrupeds,"  or,  "  Gas  is  not  heavy."  The  affirm- 
ative proposition  has  no  express  verbal  sign  or 
symbol.  The  symbols  of  the  negative  proposition 
are  not,  no,  and  none,  the  first  being  attached  to 
the  copula  or  verb,  and  the  last  two  to  the  subject 
of  the  proposition  ;  as,  "  No  trees  are  animals,"  or, 
"  None  of  the  men  was  tall." 

3.  Logico-Quantitative  Propositions.  —  Proposi- 
tions are  divided  according  to  the  quantity  ex- 
pressed by  the  subject.  The  usual  division  is  into 
Universal  and  Particular  propositions.  This  dis- 
tinction is  generally  determined  by  the  question 
whether  the  predicate  is  affirmed  or  denied  of  the 
whole  or  of  a  part  of  the  subject.  Hence  it  is  said 
that  a  Universal  proposition  is  one  in  which  the 
predicate  is  affirmed  or  denied  of  the  whole  of  the 
subject;  as,  "All  men  are  mortal,"  or,  "  No  men 
are  horses,"  and  a  Particular  proposition  one  in 
which  the  predicate  is  affirmed  or  denied  of  apart 
of  the  subject  ;  as,  "  Some  men  are  wise,"  or, 
"  Some  negroes  are  not  white." 

But  the  difficulty  with  this  definition  is  that 
there  is  a  sense  in  which  the  predicate  is  affirmed 
or  denied  of  the  whole  of  the  subject  in  the  partic- 
ular as  well  as  the  universal  proposition.  For  the 
nature  of  the  subject  may  include  what  is  known 
in  grammar  as  the  "  logical  "  subject,  which  con- 


PROPOSITIONS  77 

sists  of  all  the  terms  constituting  a  complex  con- 
ception and  standing  in  the  relation  of  "  subject" 
to  the  proposition.  In  this  sense  the  predicate 
of  a  particular  proposition  is  affirmed  or  denied 
of  the  whole  of  its  logical  subject,  but  of  only  a  part 
of  the  grammatical  subject.  If,  therefore,  we  could 
say  that  a  universal  proposition  affirms  or  denies 
the  predicate  of  the  whole  subject,  grammatical 
and  logical,  and  a  particular  proposition,  of  a  part  of 
the  grammatical  subject  only,  we  should  seem  to 
have  avoided  the  difficulty.  But  it  returns  again  in 
such  propositions  as  "All  good  men  are  worthy  of 
respect,"  which  would  be  particular  according  to 
the  definition  :  for  the  predicate  is  affirmed  of 
only  a  part  of  the  grammatical  subject. 

It  would,  therefore,  be  better  for  the  purposes  of 
definition  either  to  divide  propositions  into  Defi- 
nite and  Indefinite,  or  to  define  universal  proposi- 
tions as  affirming  or  denying  the  predicate  of  the 
whole  of  a  definite  subject,  and  particular  proposi- 
tions of  the  whole  of  an  indefinite  subject.  This 
is  what  is  actually  meant  by  the  two  kinds  of 
propositions,  and  only  technical  difficulties  in  defi- 
nition would  ever  lead  to  any  discussion  of  the 
matter.  But  with  the  condition  that  universal 
and  particular  shall  express  just  this  distinction 
between  definite  and  indefinite  subjects,  we  may 
accept  the  current  division  of  propositions  and  in- 
terpret the  common  definitions  accordingly. 

The  signs  of  the  universal  proposition,  when 
formally  expressed,  are  all,  every,  each,  any,  and 
whole,  or  words  with  equivalent  import.  The 
signs  of  particular  propositions  are  also  certain 


7 8  LOGIC   AND   ARGUMENT 

adjectives  of  quantity,  such  as  some,  certain,  a  few, 
many,  most,  or  such  others  as  denote  at  least  a  part 
of  a  class. 

But  this  twofold  division  of  propositions  into 
universal  and  particular  is  the  result  of  a  reduc- 
tion from  a  fivefold  division  which  is  frequently 
adopted  by  logicians.  Thus  propositions  are  fre- 
quently divided,  according  to  quantity,  into  Uni- 
versal, General,  Plurative,  Particular,  and  Singular. 
The  first  and  the  fourth,  Universal  and  Particular, 
are  the  same  in  definition  as  those  by  the  same 
name  in  the  twofold  division,  while  the  other  three 
may  be  treated  as  reducible  to  one  or  the  other  of 
these  two.  This  can  be  shown  as  follows  : 

A  Singular  proposition  is  one  in  which  the  sub- 
ject is  a  singular  term,  and  hence  is  quantitatively 
definite  in  its  subject ;  as,  "  Napoleon  was  a  great 
general."  Here  the  predicate  is  affirmed  of  the 
whole  of  a  definite  subject,  and  hence,  according 
to  the  definition,  it  is  possible  to  treat  the  singular 
proposition  as  a  Universal.  This  is  true,  however, 
only  in  the  formal  laws  of  the  Syllogism,  and  of 
Immediate  Inference,  but  is  not  applicable  in  the 
process  of  Opposition,  where  Singular  propositions 
must  remain  such. 

A  General  proposition  is  one  in  which  the  quan- 
titative meaning  of  the  subject  is  ambiguous  :  as 
"  Man  is  intelligent."  We  cannot  tell  from  the 
form  of  statement  whether  this  proposition  means 
that,  "y4//men  are  intelligent,"  or  that  "Men  in 
general  (normal  men)  are  intelligent."  The  prop- 
osition is  capable  of  either  interpretation,  and, 
according  as  we  think  of  all  or  some,  when  using 


PROPOSITIONS  79 

it,  is  universal  or  particular.  Formally,  it  is  only 
particular,  because  it  does  not  expressly  assert 
a//,  but  we  often  supply  this  conception  in  thought. 
For  definite  logical  purposes  all  such  propositions 
ought  to  be  reduced  to  definite  formal  expression 
to  bring  out  their  intentional  meaning  either  as 
universal  or  as  particular  propositions,  before  we 
are  safe  in  using  them  in  an  argument.  All  such 
propositions  as  the  following  are  general  :  "  Met- 
als are  useful,"  "  Trees  are  beautiful,"  "  Religion 
is  a  source  of  consolation,"  "  Diamonds  are  brill- 
iant," "  Paper  is  cheap,"  "  Governments  are  neces- 
sary." 

A  Plurative  proposition  is  one  in  which  the 
subject  is  quantified  by  most  or  an  equivalent 
term;  as  "  Most  ruminants  are  horned,"  and  re- 
quire mention  only  because  of  a  peculiar  syllo- 
gism which  is  valid  in  spite  of  its  composition  from 
particular  premises.  Plurative  propositions  are 
undoubtedly  particular.  They,  however,  affirm 
or  deny  definitely  the  predicate  of  more  than  the 
half  of  the  subject,  but  indefinitely  in  regard  to 
which  half  is  meant  by  the  term  "  most "  They 
are,  therefore,  to  be  classified  as  particular  be- 
cause they  do  not  assert  the  predicate  of  the 
whole  of  the  subject  definitely.  The  following  is 
a  general  summary  of  the  reduction  of  the  fivefold 
to  a  twofold  division  of  propositions. 

{/      Singular ji 
J-  General  . . .  -! 
Indefinite.  -,          urattve (  Particular. 
(      Particular. . . .  ) 


8o  LOGIC   AND    ARGUMENT 

Some  caution  must  be  observed  as  to  the  mean- 
ing of  several  terms  which  are  ambiguous  in  de- 
fining propositions.  Thus  the  term  all  is  equivo- 
cal. It  is  sometimes  used  collectively  instead  of 
distributively.  Thus  in  the  proposition,  "  All  the 
angles  of  a  triangle  are  equal  to  two  right  angles," 
it  means,  not  "all"  or  each  of  the  angles  taken 
separately,  but  collectively.  This  peculiarity, 
however,  does  not  affect  the  universality  of  the 
proposition. 

Again  the  term  "particular  "  does  not  denote 
an  individual  or  singular  subject.  It  often  de- 
notes this  in  common  parlance,  but  this  is  not  its 
import  in  formal  logic.  Here  it  means  an  indefi- 
nite part  of  a  whole.  This  meaning  is  explicitly 
indicated  by  the  use  of  the  term  some,  which,  in 
pure  particular  propositions  means  some  and  it 
may  or  may  not  be  all.  The  predicate  is  affirmed  of 
an  indefinite  part  of  the  subject,  and  nothing  is 
either  implied  or  stated  about  the  rest  of  this 
subject,  or  conception,  of  which  only  a  part  is  ex- 
pressly indicated  in  the  proposition. 
•  The  quality  and  quantity  of  propositions  may 
be  combined  in  the  classification  of  them,  so  that 
we  shall  have  universal  affirmative,  universal  neg- 
ative, particular  affirmative,  and  particular  nega- 
tive propositions.  It  has  been  customary  to 
denote  each  of  these  classes  by  'an  abbreviated 
symbol.  The  first  four  vowels  of  the  alphabet 
have  been  chosen  for  this  purpose — A,  E,  I,  and 
O.  The  symbol  of  the  universal  affirmative  is  A  ; 
of  the  particular  affirmative,  I  ;  of  the  universal 
negative,  E  ;  of  the  particular  negative,  O.  These 


PROPOSITIONS  8 1 

letters  shall  be  henceforth  used  for  greater  con- 
venience to  denote  their  proper  propositions.  It 
may  be  interesting  to  remark  that  A  and  I  occur 
in  the  Latin  affirmo,  and  E  and  O  in  the  Latin 
nego,  from  which  scholastic  writers  took  them  for 
mnemonic  purposes,  but  the  fact  has  no  special 
significance. 

The  following  summarizes  the  result  in  tabular 
form  : 

f  Universal..  j  Affirmative    =  A. 

|  Negative        =  E. 

Propositions . .  < 


2d.  Equivocal  Propositions. — Propositions  ob- 
tain a  double  or  equivocal  meaning  in  three  ways  : 
First,  by  the  equivocal  use  of  certain  terms  ; 
second,  by  the  inverted  position  of  certain  terms 
and  clauses  ;  and  third,  by  the  double  meaning  of 
the  proposition  as  a  whole,  even  when  there  is  no 
ambiguity  in  any  of  the  terms  composing  it.  The 
first  and  the  third  of  these  influences  affect  propo- 
sitions in  the  same  way,  giving  them  that  double 
import  which  enables  us  to  speak  of  an  implied 
proposition  as  the  complement  of  the  one  given. 
These  may  be  called  Duplex  propositions  because 
they  are  susceptible  of  analysis  into  two  distinct 
judgments.  Those  due  to  the  second  cause  may 
be  called  Inverted  propositions.  The  equivocal 
nature  of  these  propositions,  however,  whether 
duplex  or  inverted,  is  not  so  much  in  their  con- 
tent or  meaning  as  in  regard  to  their  relation  to 
6 


82  LOGIC   AND    ARGUMENT 

certain  rules  for  formal  logic.  In  the  processes 
of  reasoning  we  are  accustomed  to  treat  proposi- 
tions according  to  certain  definite  rules  regarding 
their  form  and  meaning.  In  equivocal  proposi- 
tions, however,  we  have  either  to  modify  these 
rules  or  to  reduce  these  propositions  to  their  uni- 
vocal  equivalents  before  excepting  the  meaning 
in  which  they  occur. 

i.  Inverted  Propositions. — These  are  of  two  kinds. 
First,  those  in  which  the  inversion  is  of  the  subject 
and  predicate  ;  and  second,  those  in  which  it  is  of 
some  relative  clause.  In  regard  to  the  first  of  these, 
an  example,  such  as  can  frequently  be  found  in 
poetry,  is, "Full  short  his  journey  was," or  "Great 
is  Diana  of  the  Ephesians."  In  such  cases  the  order 
of  subject  and  predicate  must  be  changed  before 
the  proposition  can  be  dealt  with  according  to  the 
formal  rules  of  reasoning  in  so  far  as  they  are  rep- 
resented in  the  ordinary  rules  of  discourse.  In 
regard  to  the  second  class,  a  part  of  the  subject 
may  sometimes  be  mistaken  for  apart  of  the  pred- 
icate, when  it  is  described  by  a  relative  clause 
standing  at  the  end  of  the  sentence  ;  as,  "  No  man 
is  honest  who  cheats  his  neighbor,"  or,  "  No  one  is 
fit  for  a  king  who  cannot  rule  himself."  The  real 
subjects  in  these  propositions  are,  "  No  one  who 
cheats  his  neighbor,"  and  "  No  one  who  cannot 
rule  himself,"  so  that  we  cannot  follow  the  rule  of 
mere  spacial  position  for  determining  them  ;  and 
hence  unless  we  keep  this  fact  in  mind  such  in- 
stances would  give  trouble  in  determining  the 
validity  of  certain  forms  of  reasoning  as  will  ap- 
pear when  that  subject  is  discussed. 


PROPOSITIONS  83 

2.  Duplex  Propositions. — A  duplex  proposition 
is  one  which  implies  a  complementary  proposition, 
and  so  requires  to  be  analyzed  into  two  distinct 
judgments.  There  are  three  kinds  :  Partitive,  Ex- 
'dusive,  and  Exceptive.  The  chief  characteristic  of 
them  is  that  the  complementary  proposition  implied  by 
them  is  of  the  opposite  quality  of  that  which  is  asserted 
in  the  given  instance.  If  the  original  proposition  be 
affirmative  the  complementary  proposition  is  neg- 
ative, and  vice-versa.  This  will  be  important  to 
keep  in  mind,  because  the  process  of  reasoning 
will  be  affected  as  much  by  the  implied  proposition 
as  by  the  original,  as  will  be  illustrated. 

(a)  Partitive  Propositions.  —  Partitive  proposi- 
tions are  those  whose  subjects  express  a  part  of  a 
whole  of  which  the  subject  of  the  implied  prop- 
osition is  the  complementary  part,  and  are  de- 
termined by  the  terms  "  Few,"  and  the  second- 
ary uses  of  "Some"  and  "Ail-not."  The  term 
"  Most "  can  also  be  included.  "  Ail-not,"  instead 
of  being  the  symbol  of  a  universal  proposition,  is 
often  conceived  as  the  same  as  "  Not-all,"  and 
hence  indicates  a  particular  proposition.  For  in- 
stance, "  All  metals  are  not  denser  than  water  " 
and  "  All  men  are  not  red-haired,"  may  mean  "  Not 
all  metals  are  denser  than,  water,"  and  "Not  all 
men  are  red-haired." 

Strictly  considered  according  to  form  of  ex- 
pression, the  original  propositions  are  E  \nform, 
but  in  matter  of  thought  they  are  I  propositions 
with  O  implied.  When  we  say  "  Not  all  men  are 
red-haired,"  or  "All  men  are  not  red-haired,"  the 
latter  being  taken  as  the  equivalent  of  the  former, 


84  LOGIC   AND    ARGUMENT 

though  formally  ambiguous,  we  mean  that  "Some 
men  are  red-haired,"  and  "  Some  men  are  not  red- 
haired."  Whichever  of  the  two  I  have  in  thought, 
the  other  is  implied. 

The  term  "  Some  "  is  subject  to  a  similar  ambi- 
guity. It  may  denote  now  " some  but  not  all"  and 
again  "some  at  least,  and  it  may  or  may  not  be  all." 
The  latter  is  the  proper  meaning  for  pure  particu- 
lar propositions,  and  the  former  is  the  meaning  for 
duplex  partitive  propositions.  Thus  the  propo- 
sitions, "  Some  metals  are  precious,"  especially  if, 
in  speaking,  the  emphasis  be  upon  the  word 
"some"  may  mean  that  "Some  metals  are  pre- 
cious," and  at  the  same  time  also  that  "  Some 
metals  are  not  precious."  This  occurs  when  the 
term  is  equivalent  to  '•''not  all"  or  "only  a  part! 
In  such  instances  it  implies  its  complementary  op- 
posite, so  that  it  means  I  and  O  at  the  same  time. 
If  the  original  be  I,  it  implies  the  simultaneous  use 
or  assumption  of  O  ;  and  if  O,  it  implies  I.  The 
proper  use  of  the  term,  however,  for  pure  particu- 
lar propositions  when  considering  the  usage  of  for- 
mal logic  in  the  processes  of  argument,  is  that  in 
which  it  denotes  "  some  and  it  may  or  may  not  be 
all" 

The  importance  of  this  will  appear  in  consider- 
ing the  subject  of  Opposition.  But  in  actual  rea- 
soning, or  the  discourse  of  actual  life,  we  must  be 
on  the  alert  for  the  ambiguity  to  which  the  term 
is  incident,  and  so  be  ready  to  detect  the  fallacy 
which  it  may  occasion. 

A  third  proposition  of  a  partitive  and  duplex 
nature  is  that  introduced  by  "  Few"  z.\\&  "  Most;" 


PROPOSITIONS  85 

as  "  Few  men  can  be  President,"  or  "  Few  cities  are 
as  large  as  Vienna,"  or  again,  "  Most  men  are  civil- 
ized." In  these  we  mean  also,  that  "  Most  men 
cannot  be  President,"  or  that  "  Most  cities  are  not 
as  large  as  Vienna,"  and  that  "  Some  men  (a  few) 
are  not  civilized."  Such  propositions  imply  a  com- 
plementary opposite,  because  the  terms  "Few  "and 
"  Most "  denote  a  part,  but  not  all.  The  expression 
"a few"  is  sometimes  synonymous  with  the  par- 
titive "few,"  and  sometimes  synonymous  with 
the  particular  "some,"  a.nd  so  varies  between  being 
a  symbol  of  partitive  and  a  symbol  of  pure  partic- 
ular propositions.  But  "few"  always  introduces 
a  proposition  which  implies  the  complementary 
opposite,  and  so  has  the  meaning  of  I  and  O  to- 
gether. 

(b)  Exclusive  Propositions.  —  Exclusive  propo- 
sitions are  introduced,  or  have  their  meaning  de- 
termined by  "on/y,"  "  alone"  and"  none  but."  They 
are,  therefore,  those  which  limit  the  predicate  to 
the  subject,  and  are  illustrated  by  such  instances 
as,  "  Only  Caucasians  are  white,"  "  Elements  alone 
are  metals,"  "  None  but  honest  men  can  be 
trusted."  When  we  say  that  "  Only  elements  are 
metals,"  we  do  not  necessarily  mean  that  "  All 
elements  are  metals  "  (for  this  might  not  be  true), 
but  that  the  class  "  metal "  belongs  exclusively  to 
the  class  "  elements,"  and  that  it  cannot  be  in  any 
class  excluded  from  that  of  "elements."  Hence 
the  meaning  of  the  proposition  is  brought  out 
either  by  its  simple  converse,  or  the  complement- 
ary opposite  proposition  which  it  implies.  The 
exclusive  proposition  must  be  reduced  to  one  of 


86  LOGIC   AND    ARGUMENT 

these  when  testing  any  special  case  of  reasoning. 
Thus,  "  Only  Caucasians  are  white,"  must  be  re- 
duced either  to  "  All  white  men  are  Caucasians," 
or  to  "All  non-Caucasians  are  not  white  "  when 
testing  the  process  of  formal  reasoning  with  such 
propositions. 

(c)  Exceptive  Propositions.  —  Exceptive  propo- 
sitions are  those  which  are  introduced  by  such 
terms  as  "  All  except"  "All  but"  "All  save"  etc. 
For  example,  "  All  except  minors  are  citizens," 
"  All  the  planets  except  Venus  and  Mercury  are 
beyond  the  Earth's  orbit."  Such  propositions  ap- 
pear to  be  universal  and  simple  at  the  same  time. 
But  they  really  consist  of  two  propositions,  which 
may  be  either  both  of  them  universal,  or  both 
particular,  or  one  of  them  universal  and  the  other 
particular.  Thus,  "  All  but  minors  are  citizens  " 
may  be  resolved  into  "  All  persons  over  twenty- 
one  years  of  age  are  citizens,"  and  "  All  under 
twenty-one  years  of  age  are  not  citizens,"  or  into 
"  Some  men  are  citizens  "  and  "  Some  men  are  not 
citizens,"  or  again  into  "All  minors  are  not  citi- 
zens," and  "  Some  persons  are  citizens."  The  first 
two  forms  of  reduction,  however,  are  preferable 
as  representing  a  better  form  of  comparison.  The 
class  of  exceptive  propositions  is  not  so  important 
for  logic  as  the  partitive  and  exclusive,  because 
their  influence  upon  fallacies  in  reasoning  is  not 
so  great. 

The  following  tabular  resume  represents  the 
divisions  of  propositions  and  the  form  to  which 
the  equivocal  forms  have  to  be  reduced  in  order 
to  be  amenable  to  the  rules  of  logic  : 


PROPOSITIONS 


Univocal 
(Simple) 


Equivocal 
(Complex) 


Logico-Grammatical 


Quanto-Qualitative 


Inverted 


Duplex 


("  Categorical. 
•<  Hypothetical. 
(.Disjunctive. 

'U"-rsa.    ]^-f4Ve- 

.™^i  £?£££"• 

Inverted  Subject  and  Predicate. 
Inverted  Relative  Clause. 


In  order  to  satisfy  the  formal  laws  of  logic,  the 
whole  class  of  equivocal  propositions  has  to  be 
reduced  to  univocal  judgments. 

III.  DISTRIBUTION  OF  TERMS.— What  is 
called  the  distribution  of  terms  in  propositions 
has  much  importance  in  determining  the  legiti- 
macy, or  at  least  the  intelligibility  of  our  reason- 
ing and  the  assurance  that  it  will  be  accepted  by 
others.  A  better  expression  would  probably  be 
the  quantification  of  terms,  but  "  distribution  "  is 
the  term  employed  by  logicians  and  it  will  be 
safer  to  abide  by  usage.  Terms  are  said  to  be 
distributed  or  undistributed  according  as  the  whole 
or  only  a  part  of  the  extension  of  a  concept  is 
taken  into  account  in  the  assertion.  A  distributed 
term  is  one  in  which  something  is  said  about  a 
definite  whole  or  about  the  totality  of  a  definite 
class.  An  undistributed  term  is  one  in  which 
something  is  said  only  about  an  indefinite  part  of 
a  whole  or  class.  Another  way  to  state  it  is  to 
say  that  distributed  term  is  one  in  which  the  con- 
ception is  definitely  quantified,  and  an  undistributed 
term  is  one  in  which  the  conception  is  indefinitely 


88  LOGIC    AND    ARGUMENT 

quantified.     Now  to  apply  these  definitions  to  the 
several  propositions,  A,  E,  I,  and  O. 

Thus  in  proposition  A,  "  All  men  are  bipeds," 
the  subject  is  said  to  be  distributed  because  the 
assertion  is  definitely  about  the  whole  of  a  class, 
or  about  a  definite  whole.  But  the  predicate  in 
the  same  proposition  is  said  to  be  undistributed, 
because  nothing  is  asserted  definitely  about  the 
whole  of  it  or  its  extension.  The  proposition  does 
not  affirm  that  "  All  men  are  all  the  bipeds,"  but 
leaves  it  free  to  suppose  that  there  may  be  other 
things  included  in  the  class  besides  "  men."  Noth- 
ing is  either  said  or  implied  to  this  effect,  and 
hence,  in  so  far  as  this  particular  assertion  is  con- 
cerned, nothing  is  known  about  the  question 
whether  the  quantity  of  the  predicate  is  greater 
or  equal  to  that  of  the  subject,  so  that  the  quan- 
tity is  wholly  indefinite,  though  certainly  equal  to 
that  of  the  subject,  but  indeterminate  beyond  this. 
Fig.  IV.  will  represent  graphically  this  relation, 


FIG.  IV.  FIG.  V. 

quantitatively  expressed,  between  subject  and 
predicate,  the  former  being  distributed  and  the 
latter  undistributed.  In  proposition  I,  for  ex- 
ample, "  Some  men  are  negroes,"  the  subject  is 
not  distributed,  because  it  is  indefinitely  quanti- 


PROPOSITIONS  89 

fied,  or  because  nothing  is  said  about  the  whole 
class  "men."  The  predicate  is  undistributed  in 
this  case  for  the  same  reason  that  it  is  in  the  A 
proposition.  The  relation  here  between  subject 
and  predicate  is  expressed  by  Figure  V.  In  propo- 
sitions E  and  O  the  quantification  of  the  subjects 
is  determined  by  the  same  rules  as  in  A  and  I, 
and  is  equally  apparent. 

But  the  quantification  of  the  predicate  in  E  and 
C-  A  is  not  so  easy  to  make  clear  in  language.  No 
term  is  employed  to  indicate  explicitly  whether 
the  whole  of  the  predicate  is  taken  into  account, 
and  we  are  left  either  to  diagrams  to  represent 
the  meaning  or  to  the  evident  import  of  the  term 
"not"  and  its  indication  of  exclusion.  Perhaps 
we  could  even  treat  this  term  as  the  quantifying 
one  in  the  case.  But  in  both  E  and  O  the  predi- 
cate is  said  to  be  distributed,  and  this  because  the 
propositions  mean  to  assert  that  the  whole  of  the 
predicate  is  excluded  from  the  subject.  The  re- 
lation between  subject  and  predicate  in  proposi- 
tion E  may  be  diagrammatically  represented  by 
Figure  VI.,  and  in  proposition  O  by  Figure  VII. 


FIG.  VI.  FIG.  VII. 


There  is  another  way  of  representing  this  rela- 
tion in  a  form  for  testing  the  validity  of  the  syllo- 


9o 


LOGIC    AND    ARGUMENT 


gism  in  formal  reasoning.  If  we  represent  the 
subject  of  a  proposition  by  S,  the  predicate  by  P, 
the  affirmative  by  the  sign  of  equality,  the  nega- 
tive by  a  cross,  the  distribution  of  a  term  by  a 
circle  around  it,  and  the  non-distribution  by  the 
absence  of  the  circle,  we  can  have  the  relations 
indicated  as  follows  :  A  propositions  will  be  rep- 
resented by  (s)  =  P ;  E  propositions  by  @  x  @  ; 
I  propositions  by  S  =  P,  and  O  propositions  by 
S  x  @. 

The  rules  for  this  quantification  may  be  formu- 
lated as  follows,  two  forms  of  statement  being 
given  for  convenience  : 

Subject.  Predicate, 

f ,,   •          .     (Affirmative,   A     Distributed,  Undistributed. 

Universal    ^Negative>       E    Distributed,  Distributed. 
Propositions  •{ 

o  _.•     i       )  Affirmative,    I     Undistributed,  Undistributed. 

[  ^articular  j  Negative.        O    Undistributed,  Distributed. 

All  Universal  propositions,  A  and  E,  distribute 
the  subject. 

All  Particular  propositions,  I  and  O  do  not  dis- 
tribute the  subject. 

All  Affirmative  propositions,  A  and  I,  do  not 
distribute  the  predicate. 

All  Negative  propositions,  E  and  O,  distribute 
the  predicate. 

There  are  two  propositions  of  a  peculiar  charac- 
ter which  require  special  mention  in  this  connec- 
tion. They  are  Definitions  and  Exclusive  proposi- 
tions. In  the  former  the  predicate  quantitatively 
coincides  with  the  subject  ;  that  is,  is  treated  as 
identical  with  it.  In  this  way  it  appears  to  be  dis- 
tributed, although  it  seems  to  be  a  universal  af- 


PROPOSITIONS  91 

firmative.  But  formally  it  is  not  so  distributed. 
We  only  know  this  equivalence  between  subject 
and  predicate  by  first  knowing  that  the  proposi- 
tion is  a  definition.  The  form  of  expression  does 
not  indicate  it  invariably  or  infallibly,  and  hence 
formally  definitions  have  to  be  treated  as  A  prop- 
ositions. When  the  predicate  is  considered  as 
distributed  in  them,  it  is  only  from  a  knowledge 
of  its  material  meaning,  and  not  from  the  mode 
of  expression,  which  is  all  that  formal  logic  can 
recognize. 

In  exclusive  propositions  of  the  form  "  Only 
elements  are  metals,"  or  "  Only  the  honest  de- 
serve respect,"  though  apparently  A  propositions, 
the  subject  is  undistributed  and  the  predicate  is  dis- 
tributed. This  is  the  meaning  of  the  term  "  only." 
In  the  case  "  Only  elements  are  metals,"  we  do 
not  say  or  imply  that  "  All  elements  are  metals," 
though  this  might  be  true.  But  we  mean  that 
"  nothing  else  "  can  be  "  metals,"  or  that  "  all  non- 
elements  are  not  metals,"  which  is  the  same  in 
meaning  as  "  All  metals  are  elements,"  in  which 
"metals"  is  distributed,  and  hence  distributed  in 
the  exclusive  proposition. 

In  this  elementary  treatise  I  shall  say  nothing 
about  the  doctrine  of  the  explicit  quantification 
of  the  predicate  as  advocated  by  some  writers,  far- 
ther than  to  say  that  it  adds  four  new  proposi- 
tions to  our  classification.  These  are  U  and  Y, 
affirmative  corresponding  to  A  and  I,  and  17  and  o> 
(Greek  letters),  negative,  corresponding  to  E  and 
O.  In  U  and  Y  the  predicate  is  said  to  be  dis- 
tributed, as  in  the  propositions  "All  the  Cau- 


92  LOGIC   AND    ARGUMENT 

casians  are  all  the  whites,"  and  "  Some  elements 
are  all  the  metals."  In  rj  and  w  the  predicate  is 
said  not  to  be  distributed,  as  "  No  men  are  some 
animals,"  and  "  Some  metals  are  not  some  ele- 
ments." Such  forms  of  expression  are  not  fre- 
quent enough  in  practical  discourse  to  treat  them 
as  important. 


CHAPTER   VI 
OPPOSITION 

I.  MEANING  OF  OPPOSITION.— Opposition 
treats  of  the  relation  between  the  propositions  A,  E, 
I,  and  O,  growing  out  of  their  quantity  and  quality. 
It  has  not  to  do  with  the  relation  between  the  sub- 
ject and  predicate,  nor  with  the  elements  of  propo- 
sitions as  such,  but  with  the  propositions  as  a 
whole.  The  question  regarding  their  consistency 
and  inconsistency  with  each  other  is  the  proper 
one  to  be  considered  in  thus  fixing  their  relations> 
and  hence  the  conditions  under  which  the.  truth  or 
falsity  of  any  one  or  more  propositions  can  be 
maintained  when  other  propositions  are  asserted. 
But  Opposition  does  not  undertake  to  decide  what 
propositions  are  necessarily  true  to  start  with,  but 
only  what  will  follow  in  three  of  them  if  the  fourth 
is  supposed  to  be  either  true,  false,  or  indetermi- 
nate. Some  propositions,  if  true,  interfere  with  the 
truth  of  others,  or  may  also  include  the  truth  of 
still  others,  and  the  falsity  of  some  propositions 
likewise  interfere  with  the  falsity  of  others,  or 
may  include  the  falsity  of  still  others.  All  four 
propositions,  assuming,  of  course,  that  they  con- 
tain the  same  matter,  cannot  be  either  true  or 
false  at  the  same  time.  Hence  the  problem  of 
93 


94 


LOGIC   AND    ARGUMENT 


opposition  is  to  determine  the  conditions  and 
limitations  under  which  any  one  or  more  of  these 
propositions  can  be  affirmed  or  denied  when  cer- 
tain others  are  affirmed  or  denied. 

We  have  said  that,  in  order  to  determine  the 
relations  of  agreement  or  disagreement  between 
these  propositions,  they  must  have  the  same  mat- 
ter. This  means  that  the  subject  and  predicate 
of  any  given  proposition  must  either  be  the  same 
as  those  of  any  others  compared  with  it,  or  must 
be  capable  of  comparison  with  such  subject  and 
predicate  through  the  relation  of  genus  or  species. 
Thus  we  cannot  determine  any  relation  of  consist- 
ency or  inconsistency  between  such  propositions 
as  "Iron  is  hard  "  and  "Water  freezes,"  or  even 
such  as  "  Iron  is  hard  "  and  "  Iron  is  useful."  We 
must  have,  for  the  purposes  of  the  purest  formal 
logic,  such  propositions  as  "  All  metals  are  ele- 
ments," "  No  metals  are  elements,"  "  Some  metals 
are  elements,"  and  "  Some  metals  are  not  ele- 
ments." In  these  alone  can  we  ascertain,  in  the 
simplest  way,  the  formal  rules  for  the  relation  of 
consistency  and  inconsistency,  between  proposi- 
tions. 

The  place  which  Opposition  occupies  in  argu- 
mentative discourse  is  this  :  It  determines  the 
manner  in  which  we  may  most  effectively  prove 
or  disprove  certain  propositions,  and  hence  the 
conditions  under  which  clear  thinking  and  debat- 
ing are  to  be  conducted.  To  this  we  shall  return 
after  exhibiting  the  laws  of  Opposition. 

II.  LAWS  OF  OPPOSITION.— The  relations 
of  consistency  and  inconsistency  between  propo- 


OPPOSITION  95 

sitions  can  first  be  illustrated  and  the  laws  for  those 
relations  formulated  afterward.  Thus  if  we  assert 
that  "All  horses  are  animals,"  it  cannot  be  true  at 
the  same  time  that  "  No  horses  are  animals,"  or  that 
"  Some  horses  are  not  animals."  This  we  express 
by  saying  that  if  A  be  true,  E  and  O  cannot  be  true 
at  the  same  time.  They  are  both  inconsistent  with  it. 
Also  again,  if  it  be  true  that  "  No  men  are  quadru- 
peds," it  cannot  be  true  that  "All  men  are  quadru- 
peds," or  that  "  Some  men  are  quadrupeds."  This 
we  again  express  by  saying  that  if  E  be  true,  A  and  I 
cannot  be  true  at  the  same  time,  but  are  inconsistent 
with  it.  But  still  farther,  if  it  be  false  that "  All  men 
are  Caucasians,"  it  will  be  true  that  "  Some  men  are 
not  Caucasians,"  but  nothing  is  determined,  one 
way  or  the  other,  about  the  proposition  "  No  men 
are  Caucasians."  This  last  may^  be  true  as  a  mat- 
ter of  fact,  but  this  truth  does  not  follow  from  the 
falsity  of  the  first.  Hence,  to  express  the  same 
matter  more  formally,  if  A  be  false,  it  follows  that 
O  must  be  true,  but  it  does  not  follow  that  E  is 
either  true  or  false.  It  is  indeterminate  so  far  as 
A  is  concerned,  no  matter  whether  it  be  true  or 
false  as  a  fact.  On  the  other  hand  again,  if  it  be 
false  that  "  Some  men  are  not  mortal,"  it  must  fol- 
low that  "  All  men  are  mortal,"  and,  as  we  have 
shown  previously,  the  negative  of  this,  "  No  men 
are  mortal,"  will  be  false.  This  we  express  by 
saying  that  if  O  be  false,  A  will  be  true  and  E  is 
false.  Similarly,  if  I  be  false,  E  must  be  true  and 
A  false.  In  this  way  we  find  that  if  A  be  true,  O 
will  be  false,  and  if  A  be  false,  O  will  be  true  ;  and 
if  E  be  true,  I  will  be  false,  and  if  E  be  false,  I  will 


96  LOGIC   AND   ARGUMENT 

be  true ;  again,  if  O  be  true,  A  will  be  false,  and  if 
O  be  false,  A  will  be  true  ;  and  if  I  be  true,  E  will 
be  false,  and  if  I  be  false,  E  will  be  true.  This 
kind  of  inconsistency  between  A  and  O,  on  the  one 
hand,  and  between  E  and  I  on  the  other,  we  call 
contradiction.  In  the  loose  sense  of  the  terms,  the 
words  "contradiction"  and  "contradictory"  are 
used  to  express  any  kind  of  inconsistency  which 
prevents  two  things  from  being  true  at  the  same 
time.  But  as  the  relation  between  A  and  E  is 
not  the  same  as  between  A  and  O  or  E  and  I,  a 
technical  meaning  has  to  be  given  to  the  term 
"contradiction"  and  another  term  employed  to 
express  the  relation  between  A  and  E.  In  the  Con- 
tradictories A  and  O,  and  E  and  I  there  is  a  mutual 
or  reciprocal  and  universal  inconsistency  which 
enables  us  to  say  that  one  or  the  other  must  be 
either  true  or  false,  or  that  only  one  of  them  can 
be  true  or  false  at  the  same  time.  But  A  and  E 
are  called  Contraries,  because,  although  the  truth 
of  A  implies  the  falsity  of  E,  and  vice  versa,  the 
truth  of  E  implies  the  falsity  of  A,  yet  the  falsity 
of  either  of  them  does  not  imply  the  truth  of  the 
other,  but  the  falsity  of  either  leaves  the  other 
wholly  indeterminate. 

It  remains  to  determine  the  relations  between 
A  and  I,  E  and  O,  and  I  and  O.  First,  if  it  be 
true  that  "  All  men  are  mortal,"  it  will  be  also 
true  that  "  Some  men  are  mortal  ;  "  if  it  be  true 
that "  No  men  are  quadrupeds,"  it  will  also  be  true 
that  "  Some  men  are  not  quadrupeds."  This  we 
express  by  saying  that  if  A  be  true,  I  must  be 
true,  and  if  Ebe  true,  O  must  be  true,  because  the 


OPPOSITION  97 

part  must  be  included  in  the  whole.  But  on  the 
other  hand,  if  it  be  true  that  "  Some  men  are 
wise,"  it  does  not  follow  that  "  All  men  are  wise  ;  " 
or  if  it  be  true  that  "  Some  men  are  not  wise,"  it 
does  not  follow  that  "  No  men  are  wise."  This 
we  express  by  saying  that  if  I  be  true,  A  will  be 
indeterminate,  and  if  O  be  true,  E  will  be  indetermi- 
nate. This  is  because  the  whole  is  not  included 
in  the  part.  But  again,  if  we  suppose  a  proposi- 
tion A  to  be  false,  it  will  be  found  that  I  will  be 
indeterminate,  and  the  same  with  O  if  E  be  false. 
On  the  other  hand,  if  I  be  false,  it  does  not  leave 
A  indeterminate,  nor  will  the  falsity  of  O  leave  E 
indeterminate.  On  the  contrary,  the  falsity  of  I 
implies  the  falsity  of  A,  and  the  falsity  of  O  that 
of  E.  This  variable  relation  is  expressed  by  call- 
ing A  and  I,  and  E  and  O,  Subalterns.  But  A  in 
relation  to  I,  and  E  in  relation  to  O  are  each 
called  Subalternans,  while  I  and  O  are  called  Sub- 
alternates. 

When  we  compare  I  and  O  we  find  that  they  are 
of  the  opposite  quality  and  the  same  quantity. 
One  is  affirmative  and  the  other  negative,  and  in 
that  respect  they  are  "  opposed  "  to  each  other. 
But  the  relation  of  consistency  and  inconsistency 
between  them  is  the  reverse  of  that  between  A 
and  E.  We  found  that  A  and  E  could  not  both 
be  true,  but  they  might  both  be  false  at  the  same 
time.  In  the  case  of  I  and  O  compared,  if  it  be 
true  that  "  Some  metals  are  elements,"  the  law  of 
Contradiction  between  E  and  I  will  make  E,  "  No 
metals  are  elements,"  false,  and  by  subalternation, 
as  just  explained,  O  will  be  indeterminate.  That 
7 


98  LOGIC   AND   ARGUMENT 

is,  nothing  follows  about  O  from  the  truth  of  I, 
and  also  nothing  about  I  from  the  truth  of  O. 
But  if  it  be  false  that  "  Some  men  are  trees,"  it 
follows  by  contradiction  that  the  proposition  "  No 
men  are  trees"  is  true,  and  by  subalternation, 
"Some  men  are  not  trees"  would  be  true  also. 
This  we  express  by  saying,  that  if  I  be  false,  E 
will  be  true,  and  by  inclusion  O  will  be  true,  and 
by  parity  of  reasoning  if  O  be  false,  I  will  be  true. 
But  both  cannot  be  false  at  the  same  time,  because 
this  would  involve  the  simultaneous  truth  of  A 
and  E,  but  they,  I  and  O,  may  both  be  true. 
This  relation  is  expressed  by  calling  them  Sub- 
contraries. 

These  various  relations  of  the  four  propositions 
can  be  diagrammatically  represented  by  what  is 
called  the  Square  of  Opposition. 

A      Contraries       E 

o  „%• 

c      °^  y      ™ 

£      fy        \p        c 
s       \&         g 

*        A,          5 

£          ^       -fc 

VJ       >O  <f  v> 

I     Subcontraries     O 

The  rules  for  regulating  or  expressing  these 
relations  can  be  formulated  as  follows : 

1.  Of  Contradictories,  one   must  be  true  and  the 
other  false. 

2.  Of  Contraries,  only  one  can  be  true  and  both 
may  be  false. 

3.  Of  Subcontraries,  only  one  can  be  false  and 
both  may  be  true. 


OPPOSITION 


99 


4.  Of  Subalterns,  if  the  subalternans  be  true,  the 
subalternate  will  be  true,  but  if  the  subalternans 
be  false,  the  subalternate  will  be  indeterminate. 
On  the  other  hand,  if  the  subalternate  be  true,  the 
subalternans  will  be  indeterminate,  but  if  the  sub- 
alternate  be  false,  the  subalternans  will  be  false. 

III.  SPECIAL  CASES.— The  rules  of  Opposi- 
tion are  laid  down  for  Universal  and  Particular 
propositions,  as  introduced  respectively  by  All 
and  Some,  or  their  equivalents.  But  they  have  to  be 
modified  for  Singular  propositions  and  for  a  class 
which  may  be  called  abstract  general  propositions, 
and  which  may  be  treated  as  Singulars.  Singular 
propositions  will  have  no  Contraries  and  no  Sub- 
contraries.  They  can  have  only  Contradictories. 
Thus,  "  Socrates  was  a  man  "  has  only  the  Con- 
tradictory "  Socrates  was  not  a  man."  The  form 
"  Some  Socrates,"  or  "  Some  of  Socrates  was  a 
man,"  is  palpably  impossible  and  nonsense,  and 
anything  more  universal  than  itself  with  the  same 
subject  is  equally  impossible.  That  it  can  only 
have  a  Contradictory  and  neither  Contrary  nor 
Subcontrary  is  evident  from  the  attempt  to  apply 
the  rules  of  Opposition  to  it.  If  the  affirmative 
be  true,  the  negative  will  be  false  ;  if  the  affirma- 
tive be  false,  the  negative  will  be  true  ;  and  vice 
versa.  This  expresses  the  relation  of  Contra- 
diction. 

What  I  have  called  abstract  general  propositions 
is  illustrated  by  such  as  "  Charity  is  a  virtue," 
"Science  is  useful,"  "  Religion  is  true."  Consid- 
ered as  abstract  terms,  the  subjects  in  these  cases 
may  be  treated  practically  as  Singulars.  Hence 


I00  LOGIC   AND   ARGUMENT 

the  rules  for  the  Opposition  of  Singular  proposi- 
tions may  also  be  applied  to  them. 

The  importance  of  these  considerations  will  be 
observed  at  once  if  we  remark  that  in  almost  all 
ordinary  discourse  and  argument  we  are  dealing 
either  with  concrete  Singular  propositions  or 
Abstract  general  ones.  The  recognition  of  this 
fact  will  simplify  the  methods  of  treating  dis- 
course. We  should  have  only  to  consider  the 
simple  relation  of  contradiction  in  the  process  of 
argument. 

IV.  PRACTICAL  APPLICATION  OF  OPPO- 
SITION.— The  practical  use  of  Opposition  con- 
sists in  its  showing  how  proof  and  refutation  can 
be  best  accomplished.  If  an  opponent  asserts  an 
A  proposition,  the  proper  and  easier  way  to  refute 
him  is  to  prove  O.  If  O  be  true,  A  cannot  be  true. 
A  could  be  equally  disproved  by  the  truth  of  E, 
but  it  is  always  harder  to  prove  a  Universal  than 
a  Particular  or  a  Singular.  Any  person  who  as- 
serts a  universal  proposition,  either  A  or  E,  lays 
himself  under  the  obligation  to  explain  away  or 
disprove  every  single  exception  brought  against 
it.  An  opponent  may  thus  always  restrict  himself 
to  the  much  easier  task  of  finding  instances  which 
contradict  the  universality  of  the  statement  against 
him,  but  if  he  takes  upon  himself  to  affirm  the  Con- 
trary instead  of  the  Contradictory,  he  lays  himself 
open  to  attack.  "  Were  it  to  be  asserted,  for  in- 
stance, that '  All  Christians  are  more  moral  than 
Pagans,'  it  would  be  easy  to  adduce  some  ex- 
amples showing  that  'Some  Christians  are  not 
more  moral  than  Pagans,'  but  it  would  be  absurd 


OPPOSITION  101 

to  suppose  that  it  would  be  necessary  to  go  to  the 
contrary  extreme,  and  show  that  '  No  Christians 
are  more  moral  than  Pagans.'  "  The  error  in  dis- 
proof, however,  may  lie  in  certain  assumptions 
about  the  relations  between  the  two  propositions 
after  the  proper  one  has  been  proved.  Thus  I 
may  be  required  to  disprove  the  proposition  "  All 
Indians  are  moral,"  and  in  order  to  do  so  I  may 
maintain,  or  prove,  that  "  Indians  are  not  civilized." 
But  here  I  simply  evade  the  issue.  My  proposition 
neither  contradicts  the  one  to  be  disproved  nor  is 
the  contrary  of  it.  Again,  it  is  no  disproof  of  the 
assertion  that  "  Cromwell  was  a  usurper,"  to  say 
that  l<  Foreign  nations  acknowledged  his  author- 
ty,"  any  more  than  it  would  be  proof  of  his  legiti- 
macy to  make  the  same  statement.  Likewise  it 
is  no  disproof  of  the  assertion  "  A  is  bad  "  to  say 
that  "  He  is  religious,"  any  more  than  it  would 
prove  that  a  man  is  white  by  showing  that  he  is 
not  black.  If  I  assert  that  "  Governments  are 
necessary,"  it  is  no  disproof  of  it  to  show  that 
"  Some  governments  are  bad."  Many  arguments 
in  refutation,  however,  are  conducted  upon  just 
such  logic,  assuming  an  inconsistency  where  there 
is  none.  But  to  be  pertinent  and  effective,  an 
argument  in  refutation  must  really  contradict,  and 
the  most  secure  resource  for  this  contradiction  is 
the  assertion  of  a  Particular  against  a  Universal 
proposition.  But  the  proof  of  a  Particular  against 
a  Particular  proposition  will  not  refute,  because, 
as  we  have  seen  in  the  Square  of  Opposition,  both 
I  and  O  may  be  true  at  the  same  time.  The  dis- 
proof in  this  case  necessitates  an  appeal  to  a  Uni- 


102  LOGIC   AND    ARGUMENT 

versal  proposition  whatever  the  disadvantages  in 
this  procedure. 

In  the  process  of  proof  as  distinct  from  refu- 
tation, there  is  no  escape  from  the  obligation  to 
use  Universals,  no  matter  whether  the  proposition 
asserted  be  a  Particular  or  a  Universal.  The 
proof  of  the  Particular  must  involve  some  Univer- 
sal or  Subalternans  which  includes  it,  and  the 
proof  of  a  Universal  involves  some  proposition 
more  general  and  inclusive  of  the  one  to  be  estab- 
lished. This  necessity  of  resorting  to  Universals 
for  proof  is  the  fact  that  makes  proof  more  diffi- 
cult than  refutation,  which,  as  we  have  seen,  does 
not  require  to  go  further  than  the  use  of  Particular 
propositions,  save  in  the  case  of  refuting  a  Partic- 
ular. But  there  is  an  alternative  here  which  con- 
siderably lightens  the  task  of  the  debater  when 
called  upon  to  argue  against  Particular  proposi- 
tions. This  is  the  demand  for  proof  of  them, 
especially  when  we  know,  what  will  be  learned  in 
discussing  the  syllogism,  that  Particular  proposi- 
tions can  serve  no  purpose  for  further  reasoning 
of  any  important  kind,  and  hence  are  serviceable 
only  for  disproof. 


CHAPTER   VII 
IMMEDIATE   INFERENCE 

I.  DEFINITION.— The  term  inference  in  gen- 
eral expresses  a  very  comprehensive  process  that 
is  difficult  to  define,  because  it  equally  includes 
the  reasoning  to  what  is  possible  with  what  is 
certain  and  necessary.  But  it  is  at  least  the  act 
of  mind  which  undertakes  to  connect  or  to  see 
new  or  old  ideas  upon  the  basis  of  those  already 
known,  and  takes  several  forms,  the  two  main  ones 
going  by  the  name  of  Deductive  and  Inductive  in- 
ference. When  it  comes  to  considering  immediate 
inference,  however,  the  definition  is  less  compre- 
hensive and,  therefore,  much  easier.  Immediate 
inference  is  simply  the  deduction  of  one  propo- 
sition from  another  implying  it.  The  process  is 
usually  defined  as  reasoning  without  a  middle  term. 
This  means  that  only  one  proposition  is  required 
for  the  premise,  and  that  the  conclusion  is  drawn 
directly  from  this  one  and  without  comparison 
with  any  other  term  or  proposition.  Thus  from 
the  proposition,  "  The  sciences  are  useful,"  I  can 
infer,  if  "  infer "  is  the  right  term  here,  that 
"  Some  useful  things  are  science,"  or,  "  What  is 
not  useful  is  not  science."  The  process  may  be 
nothing  but  a  restatement  of  the  original  meaning 
103 


IO4  LOGIC    AND    ARGUMENT 

in  a  new  form  or  relation,  but  it  nevertheless  has 
its  use  in  understanding  the  various  forms  of 
thought  which  the  mind  adopts  in  its  transition 
from  one  form  of  expression  to  another,  and  hence 
correct  immediate  inference  serves  as  a  criterion 
of  the  legitimate  mode  of  passing  from  one  propo- 
sition to  another  without  introducing  new  matter. 

II.  DIVISIONS. — The  divisions  of  Immediate 
Inference  are  based  upon  the  various  forms  in 
which  it  is  possible  to  state  directly  the  meaning 
and  implications  of  a  proposition  without  intro- 
ducing new  thought  or  ideas.  These  forms  may 
be  called,  in  terms  of  general  usage  in  logic,  Con- 
version, Obversion,  Contraversion  (Contraposition), 
Inversion,  Contribution,  and  Antithesis.  Each  of 
these  requires  separate  treatment. 

ist.  Conversion. — Conversion  is  the  transposi- 
tion of  subject  and  predicate,  or  the  process  of 
immediate  inference  by  which  we  can  infer  from 
a  given  proposition  another  having  the  predicate 
of  the  original  for  its  subject  and  the  subject  of 
the  original  for  its  predicate.  But  there  are 
certain  limitations  under  which  this  transposition 
can  take  place.  For  instance,  from  the  propo- 
sition, "All  horses  are  animals,"  we  cannot  infer 
that  "  All  animals  are  horses  ;  "  nor  that  "  Some 
animals  are  not  horses,"  though  this  may  actually 
be  a  fact.  The  rules,  therefore,  which  limit  the 
process  of  conversion  are  two  : 

(a)  The  quality  of  the  converse  must   be  the 
same  as  that  of  the  convertend. 

(b)  No  term   must  be  distributed  in  the  con- 
verse which  is  not  distributed  in  the  convertend. 


IMMEDIATE    INFERENCE  105 

These  rules  may  be  abbreviated  so  as  to  read  : 
Do  not  change  the  quality  of  a  proposition,  and  Do 
not  distribute  an  undistributed  term.  We  may  undis- 
tribute  a  distributed  term,  but  not  vice  versa.  The 
Convertend  is  the  proposition  to  be  converted  ;  the 
Converse  is  the  proposition  or  result  after  the 
process  of  conversion  has  been  performed. 

The  forms  of  conversion  are  two,  according  as 
the  quantity  of  the  Converse  is  the  same  or  differ- 
ent from  that  of  the  Convertend.  If  the  quantity 
of  the  converse  remains  the  same  as  that  of  the 
convertend,  the  conversion  is  called  Conversio  sim- 
plex, or  Simple  Conversion ;  if  the  quantity  is 
changed  (diminished),  it  is  called  Conversio  per 
accidens,  or  Limited  Conversion,  usually  Conver- 
sion by  Limitation.  We  have  now  to  illustrate  the 
process  and  to  ascertain  the  extent  of  its  applica- 
tion to  the  several  propositions,  A,  E,  I,  and  O. 

i.  Proposition  A. — Take  the  proposition,  "All 
apples  are  fruit."  In  this  proposition,  as  already 
shown,  the  predicate  is  not  distributed.  This 
means  that  other  things  also  may  be  contained  in 
the  predicate,  or  class  "  fruit,"  so  far  as  can  be 
determined  by  the  assertion  given.  It  is,  of 
course,  not  known  from  the  assertion  itself  that 
any  additional  matter  is  included  in  the  predicate, 
but  only  that  the  form  of  expression  does  not  ex- 
clude this  possibility.  Hence,  if  in  transposing 
the  subject  and  predicate,  we  say  "All  fruits  are 
apples,"  we  should  be  asserting  more  than  the 
original  proposition  will  admit.  In  the  original 
we  have  said  nothing  about  the  whole  of  the 
term  "fruit,"  whether  it  includes  or  excludes 


I06  LOGIC   AND    ARGUMENT 

other  subjects,  but  only  that  it  includes  "  apples  ; " 
and  so  we  cannot  be  permitted  to  infer  anything 
not  distinctly  said  or  implied  by  our  premise. 
Consequently,  we  can  assert  something  only  of  a 
part  of  this  predicate  in  the  process  of  conver- 
sion, if  we  assert  anything  at  all,  inasmuch  as  the 
original  asserts  something  only  of  a  part  of  the 
predicate  and  asserts  or  implies  nothing  about  the 
rest  of  it.  That  we  may  assert  something  is  evi- 
dent from  the  fact  that  some  degree  of  identity  or 
connection  exists  between  the  subject  and  predi- 
cate in  the  convertend,  and  this  same  relation  can 
be  asserted  or  inferred  in  the  converse.  By  lim- 
iting our  statement,  therefore,  to  the  part  of  the 
predicate  of  which  we  actually  affirm  something, 
we  are  able  to  infer  from  the  original  proposition 
that  "  Some  fruits  are  apples."  This  is  evidently 
legitimate,  and  as  evidently  true  if  the  original 
be  true.  Here  the  quantity  of  the  proposition  is 
changed,  while  its  quality  remains  the  same  ;  that 
is,  the  quantity  of  the  convertend  is  universal  and 
its  quality  affirmative,  while  the  quantity  of  the 
converse  is  particular  and  the  quality  affirmative. 
We  have,  therefore,  converted  A  into  I.  To  con- 
vert "  All  apples  are  fruit "  into  "  All  fruits  are 
apples,"  would  be  to  violate  the  second  rule  for 
conversion.  Hence  A  cannot  be  converted  into 
A.  To  change  the  quality  of  the  proposition  A 
in  conversion — that  is,  into  either  E  or  O — would 
be  to  violate  the  first  rule  for  conversion.  It  is 
apparent  that  we  cannot  infer  an  exclusion  be- 
tween a  subject  and  predicate  from  an  affirmed 
connection  or  identity  between  them.  Hence  A 


IMMEDIATE    INFERENCE  107 

cannot  be  converted  into  either  E  or  O,  and  we 
have  found  also  that  it  cannot  be  converted  into 
A,  but  only  into  /.  This  fact  is  expressed  by  say- 
ing that  A  is  not  capable  of  simple,  but  only  of 
limited,  conversion. 

There  is  at  least  one  apparent  exception  to  this 
rule,  and  perhaps  two.  This  is  the  case  of  defini- 
tions and  exclusive  propositions.  Definitions  are 
often  considered,  at  least  tacitly,  as  universal  af- 
firmatives, and  yet  they  are  capable  of  simple  con- 
version. The  truth  is,  however,  that  definitions 
are  not  A  propositions  in  their  meaning,  but  only 
in  their  form  of  statement.  They  are  materially 
U  propositions  and  capable  of  simple  conversion 
on  that  account,  but  formally  we  can  only  apply 
limited  conversion  to  them.  We  must  know  from 
some  other  fact  than  their  form  of  statement  that 
they  are  definitions  in  which  the  predicate  is  made 
convertible  or  identical  with  the  subject.  But 
without  assuming  this  material  identity  we  could 
know  nothing  of  the  virtual  distribution  of  the 
predicate,  and  hence  formally  definitions  have  to 
be  treated  as  all  propositions  in  A,  until  we  are 
told  or  made  to  know  the  intention  of  the  person 
using  them.  Formally  considered,  therefore,  they 
can  no  more  be  converted  than  ordinary  proposi- 
tions into  A.  Nevertheless,  it  is  important  to  ob- 
serve that  in  some  cases  of  our  actual  reasoning 
the  mind  may  be  correct  in  its  processes  on  the 
ground  that  the  datum  is  a  definition — that  is, 
subject  and  predicate  are  identical  or  convertible, 
although  formally  ;  that  is,  in  its  external  appear- 
ances, the  reasoning  is  fallacious.  It  would  simply 


I08  LOGIC   AND    ARGUMENT 

be  a  case  where  the  real  meaning  is  different  from 
the  formal  and  apparent  meaning  of  the  propo- 
sition. 

The  exclusive  proposition,  although  it  may  ap- 
pear to  some  people  as  a  universal,  is  not  such. 
The  subject  is  not  distributed,  though  the  predi- 
cate is.  The  "only"  means  some,  and  it  may  or 
may  not  be  all,  but  certainly  nothing  else.  Hence  the 
exclusive  proposition  is,  from  its  distribution  of 
the  predicate  and  not  that  of  the  subject,  in  fact 
but  an  inverted  universal,  so  that  its  simple  con- 
version is  but  its  reduction  to  an  univocal  propo- 
sition. 

2.  Proposition  /. — The  proposition  "  Some  men 
are  vertebrates  "  can  only  be  converted  into  "  Some 
vertebrates  are  men,"  or  by  simple  conversion. 
We  cannot  infer  from  it  that  "All  vertebrates  are 
men,"  for  the  same  reason  that  we  cannot  con- 
vert A  into  A.  It  is  because  the  predicate  in  the 
convertend  is  undistributed,  and  must  not  be  dis- 
tributed as  subject  in  the  converse.  It  would 
seem  to  be  an  exception  to  this  that  from  "  Some 
men  are  Caucasians"  we  maybe  supposed  to  infer 
correctly  that  "All  Caucasians  are  men."  But 
while  this  converse  may  be  true,  we  must  not  sup- 
pose that  because  any  proposition  is  true  we  can 
infer  it  from  anything  else.  We  simply  happen  to 
know  that  "All  Caucasians  are  men, "and  this  fact 
\snotf0rmally  expressed  or  implied  in  the  propo- 
sition "  Some  men  are  Caucasians  ;  "  and  as  we  are 
only  dealing  with  formally  definite  or  indefinite  as- 
sertions, we  are  not  allowed  to  transgress  our  rules 
simply  because  we  may  happen  to  know  that  any 


IMMEDIATE    INFERENCE  IOQ 

given  proposition  is  true.  We  must  distinguish 
between  what  we  can  believe  and  what  we  may  in- 
fer. Further  again,  it  would  violate  the  first  rule 
to  convert  I  into  Eor  O,  for  the  same  reason  that 
A  cannot  be  converted  into  E  or  O.  Hence  I  can 
only  be  converted  into  I.  This  is  a  case  of  Conversio 
simplex,  or  Simple  Conversion,  because  the  quan- 
tity and  quality,  or  form,  of  the  converse  is  the 
same  as  that  of  the  convertend. 

3.  Proposition  E. — The  proposition  "  No   books 
are  pens  "  can  be  converted  either  simply  or  by 
limitation.     In  this  E  proposition  the  predicate  is 
distributed,  and  this  fact  will  permit  of  the  distri- 
bution of  the  same  term  in  the  converse.     Hence 
we  can  infer  or  assert  "  No  pens  are  books."     By 
subalternation   from    this   we   can    infer  "  Some 
pens  are  not  books."     The  first  of  the  two  cases 
is  the  simple  converse,  and  the  second  the  limited 
converse  of  the  original,  and  can  be  directly  ob- 
tained by  remembering  that  a  distributed  term 
can  be  undistributed,  but  not  vice  versa.    Hence  E 
is  convertible  into  either  E  or  O.     But  O  may  be 
called  a  weakened  converse  of  E,  because  E  might 
as  well  be  inferred. 

4.  Proposition  O. — A  peculiar  difficulty  exists  in 
particular  negative  propositions,  as  will    be  ap- 
parent in  the  attempt  to  convert  the  proposition 
"  Some  men  are  not  Caucasians,"  which   is  true, 
into  "  Some  Caucasians  are  not  men,"  which  is  not 
true.     Of  course  it  is  not  the  truth  or  falsity  of 
the  converse  that  determines  whether  the  conver- 
sion is  correct  or  not,  but  we  may  safely  use  a 
contradiction  between  convertend    and  converse 


IIO  LOGIC    AND    ARGUMENT 

as  evidence  of  mistake  somewhere.  But  the  rea- 
son for  the  error  is  to  be  found  in  the  nature  of 
the  original  assertion.  First,  we  have  found  that 
the  converse  must  be  of  the  same  quality  as  the 
convertend.  In  this  case,  therefore,  the  converse 
must  be  negative.  But  according  to  the  rule, 
negative  propositions  distribute  the  predicate. 
Hence  the  subject  of  the  convertend  which  is  not 
distributed  becomes  the  predicate  of  the  converse 
which  is  distributed,  and  so  violates  the  second 
rule.  Therefore  O  cannot  be  converted  by  the 
ordinary  method,  if  at  all. 

It  has  been  usual,  however,  to  apply  what  is 
called  an  indirect  method  called  Conversion  by  Ne- 
gation. Take,  for  example,  "  Some  realities  are  not 
material  objects."  If  we  infer  that  "  Some  or  all 
material  objects  are  not  realities,"  we  violate  the 
second  rule,  because  the  predicate  of  the  converse 
is  distributed,  while  the  subject  of  the  convertend, 
which  becomes  the  predicate  of  the  converse,  is 
not  distributed.  But  now  if  we  attach  the  nega- 
tive term  "not"  to  the  predicate  in  the  original 
we  have  "  Some  realities  are  not-material,  or 
non-material  objects  ;  "  or  again,  the  equivalent, 
"  Some  realities  are  immaterial  objects."  The 
proposition  thus  resulting  is  supposed  to  be  iden- 
tical with  the  first  and  original  instance.  But  we 
observe  that  it  becomes  I  in  this  form  which  we 
can  convert  simply  into  "  Some  immaterial  objects 
are  realities,"  or  in  the  less  euphonious  form, 
"  Some  not-material  objects  are  realities."  This 
proposition,  then,  can  be  inferred  from  the  origi- 
nal, and  the  process  of  reaching  it  has  been  called 


IMMEDIATE    INFERENCE  III 

the  indirect  one  of  Negation.  The  same  process 
is  applicable  to  any  similar  propositions.  Thus 
the  instance  of  "  Some  elements  are  not  metals  " 
would  become,  first,  "  Some  elements  are  not-met- 
als,  or  non-metals,"  and  then  "Some  non-metals 
are  elements,"  etc. 

But  it  must  be  observed  that  the  quality  of  this 
so-called  converse  is  affirmative,  while  that  of  the 
convertend  is  negative,  and  hence  viewed  in  this 
light  the  process  of  conversion  by  negation  is  a 
violation  of  the  first  rule.  Besides,  we  have  been 
led  by  it  to  affirm  something  positive  about  non- 
material  or  immaterial  objects  assumed  in  the  con- 
verse, when  the  convertend  merely  denies  some- 
thing about  material  objects.  While  this  may  be 
allowable  by  some  other  process,  it  is  not  permissi- 
ble by  conversion.  The  violation  of  the  first  rule 
decides  that  matter.  Hence  we  conclude  that 
proposition  O  is  really  not  convertible  at  all,  be- 
cause the  retention  of  the  quality  violates  the 
second  rule,  and  the  alteration  of  the  quality  vio- 
lates the  first  rule.  This  is  now  the  general  opin- 
ion of  logicians.  Nevertheless,  the  process  de- 
scribed as  conversion  by  negation  is  a  legitimate 
one,  at  least  formally  speaking.  But  it  is  in  real- 
ity a  double  process :  first  one  of  obversion  and 
then  one  of  conversion,  which  makes  the  result 
the  converse  of  the  obverse  of  the  original.  This 
makes  it  what  we  shall  call  Contraversion,  or  the 
process  commonly  called  Contraposition. 

2d.  Obversion. — Obversion  is  sometimes  called 
"  Immediate  Inference  by  Privative  Conception." 
This  will  serve  as  a  good  name  when  the  propost- 


II2  LOGIC   AND   ARGUMENT 

tions  are  affirmative,  and  when  a  privative  term 
can  be  found  for  the  purpose.  But  when  the 
proposition  is  negative,  and  when  a  privative  term 
is  not  accessible,  it  is  much  better  to  use  the  term 
Obversion.  The  process  consists  in  negating  the 
copula  and  the  predicate  without  converting.  Thus 
the  proposition  "  All  men  are  mortal  "  is  obverted 
by  saying,  "  All  men  are  not  not-mortal,"  or  "  No 
men  are  not-mortal,"  or  again,  as  it  is  sometimes 
expressed,  "  No  men  are  immortal."  Here  it  is 
noticeable  that  Obversion  changes  the  quality  of  the 
proposition  in  the  process  from  affirmative  to  neg- 
ative, or  from  negative  to  affirmative,  as  the  case 
may  be.  The  meaning  of  the  original  is  retained 
by  virtue  of  the  fact  that  the  two  negatives  make  an 
affirmative,  but  the  form  of  expression  appears  as 
negative,  since  one  of  the  negatives  qualifies  the 
copula  and  the  other  the  predicate. 

In  the  negative  proposition  the  obversion  is 
accomplished  simply  by  connecting  the  negative 
particle  with  the  predicate,  which  both  changes 
the  quality  of  the  proposition  and  the  character 
of  the  predicate,  as  in  the  affirmative.  Thus, 
"  No  men  are  quadrupeds,"  or  "  All  men  are 
not  quadrupeds,"  by  obversion  becomes  "All  men 
are  not-quadrupeds,"  meaning  that  they  are  in  the 
class  "  non-quadrupeds "  from  not  being  in  the 
class  "quadrupeds."  This  process  terminates  in 
the  same  result  as  literally  following  the  rule.  To 
follow  the  rule  of  double  negation  in  this  case 
the  proposition  would  become  "  All  men  are  not 
not-quadrupeds,"  and  the  first  two  negatives  be- 
coming superfluous,  cancel  each  other  ;  so  that  we 


IMMEDIATE    INFERENCE  113 

have,  as  in  the  first  case,  "  All  men  are  not-quad- 
rupeds."  A  negative  proposition  is,  therefore,  most 
conveniently  obverted  by  transferring  the  negative 
particle  to  the  predicate.  In  regard  to  the  process 
in  general  it  will  be  found,  by  following  the  rule, 
to  apply  to  all  four  propositions — A,  E,  I,  and  O. 
3d.  Contraversion  or  Contraposition. — Contra- 
version  or  Contraposition  consists  in  the  negation 
of  copula  and  predicate  with  conversion.  That  is,  we 
first  obvert  the  original  and  then  convert  this  ob- 
verse. It  amounts  to  the  same  thing  to  take  the 
negative  of  the  predicate  in  the  contravertend  for 
the  subject  of  the  contraverse,  and  deny  the  con- 
nection between  it  and  the  subject  of  the  contra- 
vertend, if  the  latter  be  affirmative,  and  affirm 
the  connection  if  the  contravertend  be  negative. 
This  can  be  best  explained  by  an  example.  Take 
the  proposition  "All  men  are  mortal."  By  the 
very  terms  of  this  judgment  the  class  "  men  "  is 
wholly  included  in  the  class  "  mortal,"  as  indi- 
cated in  Fig.  IV.,  and  excluded,  therefore,  from 
everything  "not-mortal."  We  can,  therefore,  af- 
firm that  "  All  men  are  not  in  the  class  of  those 
who  are  not  mortal  ;  "  or,  more  briefly  the  obverse, 
"  All  men  are  not  not-mortal."  By  simple  convex 
sion  from  this  we  get  "All  not-mortal  are  not 
men."  But,  again,  noticing  that  the  inclusion  of 
"  men  "  in  the  class  "mortal  "  excludes  those  who 
are  "not-mortal"  from  "men, "we  may  as  well 
affirm  that  fact  directly,  and  hence  from  the  origi- 
nal infer  at  once  from  "  All  men  are  mortal  "  that 
"  All  not  mortals  are  not  men."  We  reach  the  re- 
sult in  this  case  without  a  roundabout  process. 
8 


H4  LOGIC   AND    ARGUMENT 

The  same  process  will  apply  to  propositions  in  E. 
Simply  include  the  negative  particle  in  the  sub- 
ject of  the  contraverse  and  make  the  latter  affirm- 
ative. Thus,  "All  negroes  are  not  Caucasians" 
will  be  contravened  by  saying  "Some  not-Cau- 
casians  are  negroes."  The  transfer  of  the  nega- 
tive particle  to  the  term  to  be  used  for  the  subject 
of  the  contravertend  has  the  effect  of  obversion, 
and  makes  the  proposition  an  A,  which  must  be 
converted  by  limitation  into  I. 

By  similar  processes  we  can  treat  I  and  O. 
But  we  shall  find  that  I  cannot  be  contravened, 
for  the  same  reason  that  O  cannot  be  converted. 
Summarizing  results,  however,  we  find  that  all 
propositions  except  O  can  be  converted  ;  all  can 
be  obverted,  and  all  except  I  contravened. 

In  the  practical  application  of  Contraversion 
we  must  be  careful  about  the  use  of  privative,  and 
especially  nego-positive,  terms.  The  result  to  the 
latter  in  particular,  in  substitution  for  the  nega- 
tion of  the  predicate,  may  lead  to  equivocation, 
and  therefore  to  material  error  in  the  process. 
Thus  to  contravert  "  All  just  acts  are  expedient  " 
into  "  All  inexpedient  acts  are  unjust,"  is  to  assume 
that  "unjust"  is  convertible  with  "  not-just,"  which 
is  not  necessarily  the  case.  A  better  illustration 
of  the  contention  here  made  is  perhaps  the  propo- 
sition "  All  human  actions  are  free,"  in  which  the 
contraverse  is  "  All  not-free  actions  are  not  hu- 
man," instead  of  "  All  not-free  actions  are  inhu- 
man" Other  cases  of  a  like  error  may  not  be  so 
evident,  but  they  are  precisely  the  kind  of  error 
against  which  we  have  to  guard. 


IMMEDIATE    INFERENCE  115 

4th.  Inversion. — Inversion  is  the  process  of  in- 
ferring from  one  proposition  another  which  shall 
contain  for  its  subject  the  negative  of  the  subject 
in  the  original,  and  for  its  predicate  the  predicate 
of  the  original.  The  result  is  accomplished  by 
alternating  the  processes  of  obversion  and  con- 
version, and  beginning  with  either  of  them  and 
proceeding  until  the  result  is  gained.  A  and  E 
can  be  inverted  ;  I  and  O  cannot.  In  the  case  of 
the  two  propositions  the  result  depends  upon  the 
way  we  begin.  Take  an  A  proposition  :  "All  horses 
are  animals."  If  we  start  with  conversion,  then 
obvert,  and  again  try  to  convert,  we  shall  find  that 
we  have  an  O  proposition  for  the  last  process  and 
we  can  proceed  no  farther.  But  if  we  first  obvert, 
then  convert,  obvert  again,  then  convert,  and  last- 
ly obvert,  we  shall  find  the  required  proposition. 
Thus,  "  All  horses  are  animals  "  obverted  is  "  All 
horses  are  not  not-animals  ;  "  then  this  converted 
gives  "All  not-animals  are  not  horses  ;  "  obverted 
again  we  have  "  All  not-animals  are  not-horses," 
and  again  converted,  being  an  A  proposition,  be- 
comes "  Some  not-horses  are  not-animals,"  and 
lastly  obverting,  we  have  "  Some  not-horses  are 
not  animals."  The  process,  however,  is  not  im- 
portant in  practical  logic  and  does  not  require  to 
be  more  than  mentioned. 

5th.  Contribution. — Contribution  is  the  process 
by  which  what  is  affixed  to  the  subject  as  a  modifier 
may  also  be  affixed  to  the  predicate  in  the  same  sense. 
It  takes  two  forms,  called  respectively  Immediate 
Inference  by  Added  Determinants,  and  Immediate 
Inference  by  Complex  Conceptions.  The  simplest 


H6  LOGIC    AND    ARGUMENT 

illustration  of  the  general  process  is  in  mathemat- 
ics.    Thus  if  x  =  a,  then  x  +  i  =  a  +  i. 

1.  Inference  by  Added  Determinants. — This  con- 
sists in  merely  adding  some  adjective  or  similar 
term  to  both  subject  and  predicate.     Thus,  to  "  A 
house  is  a  dwelling"  we  can  add  "A  good  house 
is  a  good  dwelling."     But  we  cannot  add  different 
quantities  to  both  terms,  as  is  implied  by  using  the 
superlative  degree  of  an   adjective.     Thus,  while 
we  can  say  "  Dogs  are  quadrupeds,"  we   cannot 
say  "The   largest  dogs  are  the    largest  quadru- 
peds."    The  quantity  and  quality  added  must  be 
the  same.     This  will  not  always  apply  to  particu- 
lar proportions. 

2.  Inference  by   Complex   Conception. — This   con- 
sists  in   the   addition   of    complex    phrases   and 
clauses  to  both  sides  ®f  the  proposition,  always 
observing  the  identity  of  quantity  and  quality  in 
both  cases.     Thus,  to  "  Pigeons  are  birds"  we  can 
add  "  Pigeons  that  live  in  warm  climates  are  birds 
that  live  in   warm  climates,"  etc.     But    here   we 
have  to  be  on  our  guard  against  the  same  error  as 
in  Added  Determinants.     From  "  Voters  are  men  " 
we  cannot  infer  that  '•'  The  majority  of  voters  is 
the  majority  of  men." 

False  inferences  by  contribution  often  occur, 
even  though  it  be  unintentional,  in  long  and  com- 
plicated cases  of  discourse,  and  it  requires  close 
observation  to  detect  them.  In  simple  reasoning 
they  are  not  so  liable  to  take  place. 

6th.  Antithesis. — Antithesis  isM<?  inference  from 
any  given  proposition  to  a  complementary  opposite.  It 
is  not  valid  in  any  proposition  except  materially  in 


IMMEDIATE    INFERENCE  1 17 

definitions,  and  in  duplex  propositions.  But  it  is  a 
very  common  error  to  make  the  inference.  Thus, 
if  we  make  the  assertion  that  "  All  good  men  are 
wise,"  many  people  think  themselves  entitled  to 
infer  that  "  All  bad  men  are  not  wise."  If  good- 
ness and  wisdom  are  identical,  the  inference  is 
correct,  because  the  proposition  would  practically 
be  a  definition.  But  we  know  nothing  about  such 
identity  from  the  proposition.  The  process  as- 
sumes the  distribution  of  the  predicate  when  this 
is  not  the  case.  We  must,  however,  be  on  our 
guard  also  not  to  confuse  the  mere  statement  of 
an  antithesis  with  the  inference  to  it.  Thus  the 
Book  of  Proverbs  often  states  antitheses,  which  we 
are  not  obliged  to  interpret  as  inferences  from  one 
of  the  propositions. 


CHAPTER  VIII 
MEDIATE    REASONING 

I.  DEFINITION.— Mediate  inference  is  reason* 
ing  by  means  of  a  middle  term.    A  Middle  term  is  one 
which  is  compared  with  two  others,  called  Minor 
and  Major  terms,  and  on  the  ground  of  which  a 
connection  or  relation,  affirmative  or  negative,  can 
be  established  between  these  two  in  the  conclusion. 
This  use  of  a  middle  term  makes  it  necessary  that 
there  should  be  more  than  a  single  premise  in  or- 
der to  effect  a  conclusion.     An  illustration  of  this 
form  of  reasoning  is  found  in  the  following  : 

All  machines  are  instruments  for  applying  power. 

All  locomotives  are  machines. 
.•.  All  locomotives  are  instruments   for  applying 
power. 

In  this  process  we  are  supposed  to  see  or  dis- 
cover the  connection  between  subject  and  preid- 
cate  in  the  conclusion  because  of  their  connection 
with  the  middle  term,  "  machines,"  in  the  premises. 
The  reasoning  in  such  cases  is  usually  called 
the  Syllogism,  or  Syllogistic  Reasoning. 

II.  DIVISIONS — There  are  two  kinds  of  syl- 
logistic or  mediate  reasoning,  according   as    the 
conclusion  is  or  is  not  included  in  the  premises. 
These  are  usually  called  Deductive  and  Inductive 

118 


MEDIATE    REASONING  lip 

Reasoning.  Deductive  reasoning  is  of  that  kind 
which  aims  to  deduce  the  conclusion  ;  that  is,  to 
draw  it  out  of  the  premises  by  virtue  of  its  sup- 
posed necessary  inclusion  in  them.  Inductive  rea- 
soning is  of  that  kind  which  aims  to  induce  the 
conclusion  ;  that  is,  to  suppose  a  new  idea  or  prop- 
osition as  a  probable  truth  from  known  facts.  In 
deductive  reasoning  the  premises  make  the  conclu- 
sion necessary,  supposing  that  the  formal  rules  of 
the  syllogism  have  been  observed  ;  in  inductive 
reasoning  the  conclusion  is  at  most  only  possible  or 
probable.  In  both  of  them  there  are  two  direc- 
tions, so  to  speak,  in  which  the  reasoning  may 
occur.  We  may  start  with  the  premises  and  dis- 
cover the  conclusion.  This  may  be  technically 
called  inference.  Or  we  might  start  with  the  asser- 
tion of  a  proposition  and  seek  to  discover  the 
grounds  upon  which  it  rests  ;  namely,  the  pre- 
mises. This  may  be  technically  called  proof.  The 
former  is  a  progressive,  and  the  latter  a  regressive, 
process.  In  the  one  we  discover  a  conclusion 
from  foregone  premises,  and  in  the  other  we  dis- 
cover the  premises  for  a  foregone  conclusion. 

III.  ELEMENTS  OF  THE  SYLLOGISM.— 
Every  syllogism  must  have  three  propositions  and 
three  terms,  and  only  three  of  each.  This  is  the 
simple  rule  for  the  syllogism.  The  three  terms 
are  called  the  Major,  the  Minor,  and  the  Middle 
terms.  Of  the  three  propositions,  two  are  called 
the  Premises,  and  one  the  Conclusion.  Of  the  pre- 
mises, one  is  called  the  Major  and  the  other  the 
Minor.  The  Major  term  is  the  predicate  of  the 
conclusion,  and  the  Minor  term  the  subject  of  the 


120  LOGIC   AND    ARGUMENT 

conclusion.  The  Middle  term  is  found  only  in 
the  premises,  and  may  be  either  the  subject  or  the 
predicate  in  either  of  the  premises,  but  must  al- 
ways be  found  once  in  both  premises.  The  Major 
Premise  contains  the  Major  and  Middle  Terms  : 
the  Minor  Premise,  the  Minor  and  Middle  terms  ; 
and  the  Conclusion,  the  Minor  and  Major  terms. 
Without  the  express  statement  of  the  conclusion 
there  is  no  rule  for  determining,  in  the  actual  rea- 
soning of  practical  life,  which  of  the  premises  is 
the  major  and  which  the  minor.  We  are  at  liberty 
to  choose  either  of  them  as  a  major  or  minor,  and 
to  try  the  consequences  by  the  rules  of  the  syllo- 
gism. But  for  the  sake  of  a  uniform  rule  which 
shall  express  the  most  convenient  form  in  which 
reasoning  ought  to  be  conducted  in  order  to  avoid 
obscurity,  logicians  have  agreed  to  the  law  that 
properly  the  major  premise  shall  stand  first,  the 
minor  premise  second,  and  the  conclusion  last. 
This  enables  formal  discourse  and  reasoning  to 
be  conducted  without  misunderstanding  as  to  or- 
der and  definiteness.  But  in  common  discourse 
this  rule  is  not  always  followed.  In  this  the  minor 
premise  may  come  first,  and  the  major  premise 
second  ;  or  the  conclusion  may  come  first,  as  often 
in  the  case  of  proof,  and  the  premises  in  any  order 
we  please  after  that.  But  formal  regularity  or 
uniformity  of  procedure  would  require  us  to  adopt 
some  rule  of  correct  order  in  which  the  inclusion 
of  terms  is  most  easily  perceived.  The  order  is, 
the  major  premise  first,  minor  premise  next,  and 
the  conclusion  last. 

It  has  been   usual  to  employ  symbols  for  the 


MEDIATE    REASONING  121 

several  terms  of  the  syllogism  in  order  to  illus- 
trate more  easily  the  various  relations  of  terms 
and  propositions  in  the  forms  of  reasoning.  The 
letters  chosen  for  this  purpose  are  S,  M,  and  P, 
with  an  additional  implication  in  the  use  of  S  and 
P,  as  compared  with  their  previous  employment.  S 
shall  stand  for  the  minor  term,  which  is  always  the 
subject  of  the  conclusion,  and  P  for  the  major  term, 
which  is  always  the  predicate  of  the  conclusion. 
They  thus  stand  respectively  for  the  subject  and 
predicate,  as  heretofore,  but  only  in  the  conclusion, 
since  the  minor  term,  S,  is  not  always  the  subject 
in  the  premise,  nor  the  major  term,  P,  always  the 
predicate  in  the  premise.  M  shall  stand  for  the 
middle  term,  and  may  be  either  subject  or  predicate 
in  either  or  both  of  the  premises.  The  combina- 
tion of  these  terms  will  represent  the  premises  and 
conclusion. 

Terms. 

M  =  Middle  Term. 

S   =  Minor  Term  =  Subject  of  Conclusion. 

P  =  Major  Term  =  Predicate  of  Conclusion. 

Propositions. 

M  is  P  =  Major  Premise. 
S  is  M  =  Minor  Premise. 
S  is  P  =  Conclusion. 

IV.  RULES  FOR  THE  SYLLOGISM.— The 

rules  for  the  construction  of  the  syllogism  may  be 
divided   into   two  classes.     First,  those  affecting 


122  LOGIC   AND    ARGUMENT 

the  subject-matter  of  the  propositions  and  the 
syllogism  as  a  whole.  Second,  those  affecting 
the  quantity  and  quality  of  the  propositions.  We 
do  not  investigate  here  how  these  rules  came  to 
be  adopted,  as  the  reasons  for  them  would  take 
us  farther  than  an  elementary  treatise  will  allow. 
Hence  we  simply  state  the  results  with  the  pur- 
pose of  using  the  rules  to  test  the  valid  and  in- 
valid forms  of  reasoning. 

i  st.  Rules  Affecting  the  Subject-Matter  of  the 
Syllogism. 

1.  Every  syllogism  must  have  three  terms,  and 
only  three  terms. 

2.  Every   syllogism    must   have  three  proposi- 
tions, and  only  three  propositions. 

3.  No  term  in  the  premises  of  the  syllogism 
should  be  ambiguous. 

An  ambiguous  term  is  equivalent  to  the  use  of 
four  terms  in  the  syllogism.  Although  it  con- 
forms in  appearance  to  the  rule,  its  double  mean- 
ing makes  it  include  the  fourth  term. 

ad.  Rules  Affecting  the  Quantity  and  Quality 
of  Propositions. 

4.  The  middle  term  must  be  distributed  at  least 
once  in  the  premises. 

5.  No  term  must  be  distributed  in  the  conclu- 
sion which  was  not  distributed  in  the  premises. 

6.  No   conclusion    can    be   drawn    when    both 
premises  are  negative. 

7.  No   conclusion   can   be   drawn    when    both 
premises  are  particular. 

8.  No  universal  conclusion  can  be  drawn  when 
one  of  the  premises  is  particular  ;  or  if  one  of  the 


MEDIATE    REASONING  123 

premises  be  particular,  the  conclusion  must  be- 
particular. 

9.  No  affirmative  conclusion  can  be  drawn 
when  one  of  the  premises  is  negative  ;  or  if  one  of 
the  premises  be  negative  the  conclusion  must  be 
negative. 

In  the  construction  of  every  syllogism  we  must 
have  reference  to  two  things  :  first,  the  quantity 
and  quality  of  the  propositions,  and  second,  the 
position  of  the  middle  term.  These  conditions 
give  rise  to  what  are  called  the  Moods  and  the 
Figures  of  the  syllogism. 

V.  MOODS  OF  THE  SYLLOGISM.— The  Mood 
of  a  syllogism  is  that  characteristic  of  it  which  is 
determined  by  the  quantity  and  quality  of  its  propo- 
sitions. The  Mood  can  never  be  separated  from 
the  Figure  in  practical  reasoning,  but  it  is  not 
determined  by  the  same  characteristics.  Every 
syllogism,  as  we  have  seen,  must  contain  three 
propositions  and  only  three.  But  there  are  four 
forms  of  propositions  (eight  in  case  of  quantify- 
ing the  predicate)  to  be  considered,  from  which 
three  have  to  be  chosen  and  combined  in  various 
ways.  Thus  all  three  propositions,  major  premise, 
minor  premise,  and  conclusion  may  be  A  propo- 
sitions, or  one  an  A  or  I  proposition,  one  E  and 
the  other  an  E  or  O,  etc.  With  the  four  propo- 
sitions, therefore,  the  conceivable  Moods  will 
represent  all  possible  combinations,  either  of  the 
same  or  different  quantity  and  quality.  When  the 
combinations  are  completed  we  find  them  to  be 
sixty-four  in  number.  They  appear  in  the  follow- 
ing table  : 


124 


LOGIC   AND    ARGUMENT 


AAA  AEA  AIA  AOA  EAA  EEA  EIA  EGA 

AAE  AEE  AIE  AOE  EAE  EEE  EIE  EOE 

AAI  AEI  All  AOI  EAT  EEI  EII  EOI 

AAO  AEO  AIO  AGO  BAG  EEO  ElO  EGO 


IAA  IEA  IIA 

IAE  IEE  HE 

IAI  IEI  III 

IAO  IEG  IIO 


IOA     OAA  OEA  OIA  OOA 

IOE     OAE  GEE  OIE  OOE 

IOI      OAI  OEI  Oil  OOI 

IOO    OAO  OEO  OIO  OOO 


But  these  are  not  all  valid  forms  of  reasoning. 
Some  of  them  violate  one  rule,  some  another,  and 
some  even  two  rules.  For  example,  EEA  violates 
rule  6,  and  IIA  violates  rule  8,  and  IOA  rules  8 
and  9.  By  applying  the  several  rules,  including. 
6,  7,  8,  and  9,  to  this  table  we  are  enabled  to  re- 
ject all  but  tivelve  of  these  Moods,  as  violating  one 
or  the  other  of  these  rules,  and  as  not  possibly 
valid  in  any  case.  The  twelve  Moods  remain  as 
possibly  valid,  though  they  must  first  be  tested  by 
rules  4  and  5  before  they  can  be  accepted,  and  it 
will  be  found  that  some  of  them  are  valid  in  one 
Figure  of  the  syllogism  and  not  in  another,  while 
one  of  them  will  be  found  to  be  invalid  in  all  of 
them.  This  is  IEO.  The  possible  Moods,  how- 
ever, remaining  after  applying  the  last  four  rules 
to  the  whole  table  are  as  follows  : 


AAA 

AAI 

All 

AEE 

AEO 

AOO 


EAE        IAI 
EAO      (IEO) 
EIO 


OAO 


MEDIATE    REASONING  125 

These  remain  to  be  tested  in  the  four  Figures,  so 
that  there  will  be  forty-eight  forms  still  to  consider. 

VI.  FIGURES  OF  THE  SYLLOGISM.— The 
Figure  of  a  syllogism  is  that  characteristic  of  it 
which  is  determined  by  the  position  of  the  middle 
term.  As  there  are  two  propositions,  each  with  a 
subject  and  predicate,  in  the  premises  of  every 
syllogism,  there  are  four  possible  positions  for 
the  middle  term.  It  may  be  the  subject  of  both, 
the  predicate  of  both,  the  subject  of  the  major 
and  predicate  of  the  minor,  or  the  predicate  of 
the  major  and  the  subject  of  the  minor  premise. 
These  positions  and  the  several  Figures  are  rep- 
resented in  the  following  diagram  : 

FIG.    I.  FIG.  II.  FIG.  III.  FIG.    IV. 

M  =  P       P  =  M      M=P       P=M 

S  =  M      S  =  M      M  =  S      M  =   S 
S  :=  P       S  =  P        S  =  P       S-P 

The  twelve  possible  Moods  have  to  be  tested 
in  each  of  these  Figures  before  we  know  the  con- 
ditions under  which  they  are  valid  at  all.  By 
applying  the  rules  for  the  distribution  of  terms 
and  the  limitations  upon  correct  reasoning,  as 
determined  by  rules  4  and  5,  we  find  that  some  of 
the  twelve  moods  are  valid  in  each  Figure  and 
some  are  not.  Thus  we  have  an  illustration  of 
this  method  in  the  mood  AAA  for  all  the  Figures. 

FIG.  I.  FIG.  II.  FIG.  III.  FIG.  IV. 

A   (g)=P  A  (P)=M  A   (M)=P  A  (P)  =  M 

A   (S}=M  A    (|)=M  A    ®=S  A   ©  =  S 

A  (S)-P  A   (D=P  A   (S)=P  A  (S)  =  P 

VALID.  INVALID.  INVALID.  INVALID. 


126  LOGIC    AND    ARGUMENT 

In  the  first  Figure  the  rules  for  distribution  are 
satisfied,  and  AAA  is  valid.  But  in  the  second 
Figure  the  middle  term  is  not  distributed  in  either 
premise,  and  the  fallacy  is  called  Undistributed or 
Illicit  Middle,  In  the  third  Figure  the  minor 
term  is  not  distributed  in  the  minor  premise,  but 
is  distributed  in  the  conclusion.  This  gives  an 
Illicit  Minor.  In  the  fourth  Figure  the  same  fal- 
lacy is  committed,  and  hence  AAA  is  valid  in 
only  one  Figure.  By  applying  the  same  test  to  all 
the  twelve  Moods  in  the  four  Figures  we  have 
the  following  as  the  valid  and  the  invalid  Moods 
in  each  Figure.  A  line  is  drawn  across  those  that 
are  invalid. 


AAA 

AAI    A**  AAI  AAI 

All    ***  All  Arrt 

AEE  AEE  AEE 

AEO  A66  AEO 
AGO 

EAE    EAE 

EAO   EAO  EAO  EAO 

EIO    EIO  EIO  EIO 

IAI  IAI 


OAO   OAO   OAO 


Six  Moods  are  valid  in  each  Figure  and  six  are 
invalid,  so  that  we  have  in  this  representation  a 
measure  of  the  combination  of  propositions  and 
forms  of  reasoning  that  are  legitimate. 


MEDIATE    REASONING  127 

If  we  observe  this  list  we  shall  notice  that  the 
First  Figure  is  the  only  one  which  will  give  a  uni- 
versal affirmative  conclusion,  and  it  is  the  only  one 
which  will  give  conclusions  in  all  four  propositions, 
A,  E,  I,  and  O.  The  Second  Figure  gives  only 
negative  conclusions,  and  the  Third  Figure  gives 
only  particular  conclusions.  The  Fourth  Figure 
has  never  been  regarded  as  important  enough  in 
argument,  being  so  little  used,  to  receive  any  at- 
tention from  logicians,  though  it  gives  conclusions 
in  E,  I,  and  O.  We  have  only  to  mutate  or  trans- 
pose the  premises  of  the  Fourth  Figure  in  order 
to  produce  the  First  Figure. 

VII.  REDUCTION  OF  MOODS  AND  FIGURES. 
— The  First  Figure  of  the  syllogism  is  the  most 
natural  form  for  most  of  our  reasoning,  at  least 
when  we  are  not  engaged  in  the  process  of  dis- 
proof. Consequently,  looking  at  the  perplexing 
number  of  Moods  and  Figures  that  are  valid,  the 
old  logicians  sought  to  reduce  the  various  Moods 
in  the  other  Figures  into  the  valid  forms  of  the 
First.  The  process  is  a  rather  complicated  one 
and  has  no  practical  importance,  and  is  impossi- 
ble, directly,  in  the  Moods  AOO  of  the  Second 
Figure,  and  OAO  of  the  Third  Figure.  But 
without  going  through  the  scholastic  method  of 
reduction,  and  without  guaranteeing  that  the 
method  of  reduction  here  indicated  will  result  al- 
ways in  valid  equivalents  after  the  process  has 
been  accomplished,  I  may  suggest  a  few  simple 
rules  for  the  reduction  of  the  Moods  in  one  Figure 
to  those  of  another.  The  whole  process  can  be 
effected  by  the  proper  adjustment  of  conversion  and 


128  LOGIC   AND    ARGUMENT 

mutation  of  premises.  Thus,  convert  the  major 
premise  of  the  First  Figure,  and  we  obtain  a  syllo- 
gism of  the  Second  Figure.  Convert  the  major 
of  the  Second  and  we  obtain  the  First  Figure. 
Mutate  the  premises  in  either  the  First  or  Fourth 
Figure  and  we  obtain  the  other,  etc. 

VIII.  PRACTICAL  IMPORTANCE  OF  THE 
FIGURES. — There  is  some  difference  between  the 
various  Figures  in  regard  to  their  practical  value. 
In  the  first  place,  they  cannot  all  be  applied  to  at- 
tain the  same  result,  the  Second  Figure  giving  no 
affirmative,  and  the  Third  Figure  no  universal  con- 
clusion. The  First  Figure  is  the  most  natural  and 
the  most  usual  form  of  reasoning,  and  is  regarded 
by  logicians  as  the  Figure  best  adapted  to  proof, 
especially  as  it  will  give  all  four  propositions,  A,  E, 
I,  and  O,  in  its  conclusion,  and  is  the  only  one  in 
which  universal  affirmatives  are  possible,  which 
represent  the  most  important  forms  of  conviction. 
Again,  the  First  Figure  being  the  most  natural 
and  the  most  usual  form  of  reasoning,  it  is  inter- 
esting to  remark  that  argument  is  not  possible  in 
it  with  a  particular  major  premise,  or  a  negative 
minor  premise.  Hence,  the  rule  that  we  are  liable 
to  fallacy  unless  our  major  premise  is  universal,  a 
fact  which  is  true  for  all  the  Figures  except  IAI 
in  Figs.  III.  and  IV.,  and  OAO  in  Fig.  III.  As 
these  two  Moods  are  perhaps  never  used  in  prac- 
tical life,  and  the  Figures  very  seldom,  we  can 
dismiss  them  and  accept  the  rules  as  practically 
universal.  In  an  argument,  therefore,  involving 
proof,  we  must  see  that  our  premises  are  universal 
if  we  wish  to  establish  a  universal  conclusion. 


MEDIATE    REASONING  129 

The  Second  Figure  is  best  adapted  to  disproof, 
or  refutation.  It  is  so  adapted,  partly  because 
one  of  the  premises  must  be  negative,  and  chiefly 
because  of  the  nature  of  the  comparison  which 
can  be  instituted  between  the  subject  and  predi- 
cate. It  is  evident  that  two  things  which  cannot 
agree  in  their  predicate  cannot  agree  with  each 
other.  In  the  First  Figure  a  disagreement  be- 
tween the  subject  of  one  and  the  predicate  of  the 
other  premise  leads  to  fallacy.  Hence,  in  order  to 
disprove  an  assertion,  we  have  only  to  show  that 
one  instance,  or  more,  included  in  the  general 
statement,  does  not  agree  with  the  predicate,  and 
we  have  the  contradictory  established.  For  in- 
stance, if  the  assertion  is  made  that  "  All  forms 
of  government  are  beneficial,"  it  is  evident  by 
subalternation  that  "  Despotic  governments  (some 
governments)  are  beneficial,"  though  the  assertor 
may  not  consciously  recognize  the  fact  when  he 
makes  the  statement.  Hence,  the  opponent  may 
assert  and  prove  (by  the  First  Figure,  EAE) 
that  "  Despotic  governments  are  not  beneficial." 
This  last  proposition  will  be  the  minor  premise  of 
a  syllogism  of  which  the  major  premise  is  the 
first  proposition.  This  would  give  the  conclusion, 
"  Despotisms  are  not  forms  of  government,"  a 
conclusion  which  contradicts  what  is  implied  by 
the  subalternate  of  "  All  governments  are  benefi- 
cial," and  so  contradicts  the  original  assertion. 
The  affirmative  will  thus  either  have  to  give  up 
his  allegation  or  show  that  "  Despotisms  are  not 
forms  of  government,"  and  thus  admit  the  possi- 
bility that  they  are  not  beneficial  without  suppos- 
9 


130  LOGIC    AND    ARGUMENT 

ing  the  contradiction  indicated.  The  former  posi- 
tion accepts  the  refutation  ;  the  latter  has  to 
meet  an  equivocation  in  the  use  of  terms  which  is 
at  least  almost  as  fatal  as  a  contradiction. 

The  Third  Figure  is  adapted  to  the  proof  of 
exceptions  to  universals,  and  so  may  use  its  result 
for  the  disproof  of  some  universal  assertion. 
Suppose  someone  asserts  that  "  No  philosophers 
are  wise."  The  easiest  disproof  of  this,  as  we 
have  seen,  lies  in  the  proof  of  the  contradictory  I. 
We  have  then  only  to  take  some  syllogism  in  the 
Third  Figure  with  this  proposition  as  its  conclu- 
sion ;  as  follows  : 

Plato,  Kant,  etc.,  were  wise. 
Plato,  Kant,  etc.,  were  philosophers. 
.*.  Some  philosophers  were  wise. 

Here  we  both  prove  that  "  Some  philosophers 
are  wise,"  and  disprove  the  universal  negative  of 
the  same  proposition,  assuming,  of  course,  that 
our  premises  are  true. 

The  Fourth  Figure  is  not  regarded  by  logicians 
as  having  any  practical  value. 


CHAPTER    IX 

SIMPLE   AND   COMPLEX   FORMS    OF   CATEGOR- 
ICAL  REASONING 

I.  CLASSIFICATION  OF  FORMS.— The  syl- 
logism as  it  has  been  explained  was  the  simple 
syllogism  of  three  propositions.  All  arguments 
can  be  reduced  to  this  simple  form,  but  while  this 
is  the  fact  much  of  our  reasoning  takes  on  a  more 
complex  form.  Some  propositions  may  be  omit- 
ted in  formal  and  explicit  expression,  though  in- 
cluded in  the  thought  of  the  reasoner,  and  in 
other  cases,  while  the  premises  of  the  main  argu- 
ment are  explicitly  stated,  they  are  complicated 
with  various  propositions,  stated  or  implied,  that 
are  intended  to  prove  them  instead  of  merely  as- 
serting them.  This  introduces  at  least  implied 
syllogisms  into  the  discourse,  which  are  subordi- 
nated to  the  main  purpose.  These  two  circum- 
stances give  rise  to  two  divisions  of  the  syllogism. 
They  are  the  Complete  and  Incomplete,  each  with 
the  subdivisions  Simple  and  Complex.  The  com- 
plete syllogism  represents  an  explicit  statement 
of  all  that  is  involved  in  the  mental  process.' 
This  may  not  often  occur  in  ordinary  discourse, 
and  when  it  does  it  is  not  likely  to  follow  the 
formal  expression  which  has  been  explained  in  the 


132  LOGIC    AND    ARGUMENT 

Moods  and  Figures.  The  usual  mode  of  argu- 
ment is  either  to  state  the  facts,  leaving  the 
hearer  to  draw  the  inference,  or  to  state  only  one 
of  the  premises,  leaving  the  other  to  be  under- 
stood. But  where  it  is  necessary  to  be  clear  and 
explicit  we  formulate  the  argument  into  complete 
syllogisms  of  some  form.  They  may  all  be  classi- 
fied as  follows  : 


Syllogisms 


1  ,        f  Simple  =  Ordinary  form, 
-ompiete..  |  Complex  =  Prosyllogism  and  Episyllog 


I  Simple  =  Enthymeme 

Incomplete  •{  ,  .  c.     , 

Epicheirema.jS.ngl. 

Complex  =    \ 

I-                           I  Sorites  \  Progressive. 

lbontes \  Regressive. 


II.  EXPOSITION.  —  The  classification  has 
shown  us  one  simple  and  two  complex  forms  of 
reasoning  to  be  considered  that  have  not  been 
noticed.  They  are  all  reducible  to  the  rules  and 
form  of  the  simple  complete  syllogism. 

ist.  Prosyllogism  and  Episyllogism.  —  The 
Prosyllogism  and  Episyllogism  consists  of  two 
syllogisms,  the  conclusion  of  the  first  being  a  pre- 
mise in  the  second.  The  following  are  illustra- 
tions, the  one  abstract  and  the  other  concrete  : 

A  is  B  Men  are  vertebrates. 

C  is  A  Europeans  are  men. 

.'.  C  is  B  .•.  Europeans  are  vertebrates. 

D  is  C  Italians  are  Europeans. 

.•.  D  is  B  .*,  Italians  are  vertebrates. 


FORMS   OF    CATEGORICAL    REASONING  133 

2d.  Enthymeme. — An  Enthymeme  is  an  incom- 
plete syllogism  in  which  one  of  the  premises,  or 
the  conclusion,  may  be  omitted.  If  the  major 
premise  be  omitted,  the  enthymeme  is  of  the  first 
order  ;  if  the  minor  premise  be  omitted,  the  enthy- 
meme is  of  the  second  order  ;  and  if  the  conclu- 
sion be  omitted,  the  enthymeme  is  of  the  third 
order.  The  signs  of  it  are  such  words  as  indicate 
that  a  reason  is  given  for  the  truth  of  the  prop- 
osition asserted.  These  words  are  for,  because, 
since,  inasmuch  as,  and  in  the  conclusion,  therefore, 
consequently,  etc.  As  an  illustration  we  have  the 
propositions  :  "  The  air  must  have  weight,  be- 
cause it  is  a  material  substance."  The  conclusion 
in  this  instance  is  the  statement,  "  The  air  must 
have  weight."  If  we  were  stating  a  mere  fact  not 
looking  to  any  further  result,  it  might  not  require 
proof,  but  we  often  desire  to  support  an  assertion 
by  reasons  that  will  show  its  truth  apart  from 
mere  acceptance  on  authority.  In  the  above  in- 
stance, the  major  premise  is  omitted,  and  is  "All 
material  substances  have  weight."  When  reduced, 
the  enthymeme  becomes  a  simple  complete  syllo- 
gism. 

There  are  forms  of  the  enthymeme  in  which  the 
signs  are  not  expressed,  but  which  have  to  be  de- 
termined by  the  evident  relation  of  the  thoughts 
stated.  The  definite  and  explicit  use  of  the  signs 
often  give  a  stilted  and  formal  appearance  to  dis- 
course, and  hence  rhetorical  reasons  may  be  sus- 
tained for  omitting  them.  The  intended,  or  at 
least  the  implicit,  reasoning  in  such  cases  must  be 
discovered  from  the  actual  dependence  logically 


134  LOGIC    AND    ARGUMENT 

of  one  thought  upon  another.  Hence,  in  much  of 
the  discourse  that  does  not  formally  profess  to  be 
reasoning  we  shall  find  that  process  tacitly  indi- 
cated, and  it  must  be  adjudged  accordingly. 

3d.  Epicheirema. — An  epicheirema  is  a  syllo- 
gism in  which  one  or  both  of  the  premises  is  sup- 
ported by  a  reason  which  implies  an  imperfectly 
expressed  syllogism  ;  in  other  words,  it  is  a  syllo- 
gism in  which  one  or  both  of  the  premises  is  an 
enthymeme  of  the  first  or  of  the  second  order. 
The  epicheirema  may  be  single  or  double.  It  is 
single  when  only  one  of  the  premises  is  an  enthy- 
meme ;  it  is  double  when  both  premises  are  en- 
thymemes.  Following  are  illustrations  : 

Single. 
A  is  B  ;  for  it  is  P.  Vice  is  odious,  for  it 

depraves. 

C  is  A.  Avarice  is  a  vice. 

.'.  C  is  B.  .-.  Avarice  is  odious. 

Double. 

A  is  B  ;  for  it  is  P.  Man  is  rational  be- 

cause    he    has    a 
mind. 

C  is  A,  for  it  is  Q.  Europeans  are  men, 

because  they  are 
civilized. 

.*.  C  is  8.  .'.Europeans      have 

minds. 

The  single  epicheirema  when  reduced  to  a 
complete  form -becomes  a  prosyllogism  and  epi- 
syllogism,  or  two  syllogisms.  The  double  epi- 


FORMS   OF    CATEGORICAL    REASONING  135 

cheirema,  when  completed,  becomes  three  syllo- 
gisms, representing  two  prosyllogisms  and  two 
episyllogisms,  one  of  the  three  being  both  a  pro- 
syllogism  and  an  episyllogism,  the  former  in  rela- 
tion to  the  following  and  the  latter  in  relation  to 
the  preceding  syllogism.  An  illustration  of  this 
is  the  following  : 

(       Whatever  has  a  mind  is  rational 
ind<       Man  has  a  mind. 
(  .'.  Man  is  rational. 


Man  is  rational,  for  he  has  a  mi 


Europea 
.'.  Europe 


(       Whatever  is  civilized  is  man. 
ans  are  men,  for  they  are  civilized  •<       Europeans  are  civilized. 

/  .'.  Europeans  are  men. 
ans  are  rational. 


4th.  Sorites.  —  A  sorites  is  so  called  because  the 
propositions  constituting  it  form  what  is  regarded 
as  a  "  chain,"  or  a  continuous  series,  of  premises 
from  which  a  conclusion  is  drawn  at  the  end  of 
the  series,  but  not  before.  It  consists  of  enthy- 
memes  of  the  third  order,  as  the  epicheirema  con- 
sists of  enthymemes  of  the  first  and  second  order. 
When  completed,  therefore,  the  sorites  also  forms 
a  prosyllogism  and  an  episyllogism,  or  a  number 
of  them.  To  complete  it  we  have  only  to  supply 
the  omitted  conclusion.  The  form  of  the  sorites 
is  twofold,  Progressive  and  Regressive.  The  fol- 
lowing are  illustrations  : 

Progressive  Series. 

A  is  B.  Bucephalus  is  a  horse. 

B  is  C.  A  horse  is  a  quadruped. 

C  is  D.  A  quadruped  is  an  animal. 

D  is  E.  An  animal  is  an  organism. 

.*.  A  is  E.  .*.  Bucephalus  is  an  organism. 


136  LOGIC   AND    ARGUMENT 

Regressive  Series. 

A  is  B.  An  animal  is  an  organism. 

C  is  A.  A  quadruped  is  an  animal. 

D  is  C.  A  horse  is  a  quadruped. 

E  is  D.  Bucephalus  is  a  horse. 

.-.  E  is  B.  /.  Bucephalus  is  an  organism. 

The  difference  between  the  progressive  and  the 
regressive  sorites  is  only  one  of  form  in  statement, 
not  in  the  form  of  reasoning.  The  sorites  may 
also  be  divided  into  the  constructive  and  the  de- 
structive. It  is  constructive  when  the  conclusion 
is  affirmative  j  destructive  when  the  conclusion  is 
negative.  The  above  illustrations  are  of  the  con- 
structive form  and  represent  the  propositions  as 
all  of  them  universal  affirmative,  hence  of  the 
Mood  AAA.  But  there  are  two  more  constructive 
Moods,  AAI  and  All,  and  three  destructive  Moods, 
EAE,  EAO,  and  EIO,  all  six  being  of  the  First 
Figure. 

The  rules  for  the  valid  forms  of  the  sorites 
should  be  stated,  because  the  number  of  cases  in 
which  this  mode  of  reasoning  is  legitimate  is  ex- 
ceedingly limited.  Any  number  of  premises  may 
be  used,  but  the  quantity  and  quality  of  the  prop- 
ositions constituting  them  are  under  strict  limi- 
tations. The  rules  regulating  their  construction, 
therefore,  are  two,  and  are  as  follows  : 

1.  Only  one  premise  can  be  negative,  and  this 
must  be  the  prime  major. 

2.  Only  one  premise  can  be  particular,  and  this 
must  be  the  final  minor. 

Since  the  sorites  is  an  incomplete  prosyllogism 


FORMS    OF    CATEGORICAL    REASONING  137 

and  episyllogism,  there  are  intermediate  major  and 
minor  premises.  The  prime  major,  therefore,  will 
be  the  last  premise  in  the  progressive,  and  the  first 
premise  in  the  regressive,  series.  The  final  minor 
will  be  the  first  premise  in  the  progressive  and 
the  last  in  the  regressive  series.  If  any  other 
premise  than  the  prime  major  be  negative,  the 
Mood  being  AEE,  there  will  be  a  fallacy  of  illicit 
major,  and  if  any  other  premise  than  the  final 
minor  be  particular,  the  Mood  being  IAI,  there 
will  be  a  fallacy  of  illicit  or  undistributed  middle. 


CHAPTER   X 
HYPOTHETICAL    REASONING 

I.  NATURE  AND  DIVISIONS.— We  have  al- 
ready seen  that  there  are  three  kinds  of  proposi- 
tions which  correspond  to  as  many  kinds  of  rea- 
soning. These  propositions  are  the  Categorical, 
Hypothetical,  and  Disjunctive,  and  the  forms  of 
reasoning  go  by  the  same  name.  A  categorical 
syllogism  is  one  in  which  all  the  propositions  are 
categorical.  A  hypothetical  syllogism  is  one  in 
which  one  or  more  of  the  premises  are  hypotheti- 
cal. The  main  object  of  the  latter  is  to  secure  a 
conditional  conclusion,  if  not  in  its  form  of  state- 
ment, certainly  in  its  subject-matter.  In  categori- 
cal propositions  and  syllogisms  we  usually  mean  to 
assume  or  to  assert  the  truth  of  our  premises,  and 
if  our  formal  reasoning  be  correct  we  can  accept 
the  conclusion  as  a  true  proposition.  But  often 
we  wish  first  to  bring  out,  if  only  conditionally, 
the  truth  upon  which  a  proposition  rests,  so  as 
to  see  if  the  connection  between  this  conclusion 
and  the  major  premise  be  admitted.  The  whole 
question  will  then  depend  upon  the  manner  of 
treating  the  minor  premise.  This  has  the  advan- 
tage of  getting  the  major  premise  admitted  with- 
out the  formal  procedure  of  proof,  and  the  minor 
premise  is  usually  more  easily  proved  than  the 
138 


HYPOTHETICAL    REASONING  139 

major.  Consequently,  one  is  made  to  see  more 
clearly  the  force  of  the  argument  or  reasoning  by 
removing  the  question  of  the  material  truth  of  the 
major  premise  and  concentrating  attention  upon 
the  relation  between  the  conclusion  and  its  condi- 
tions, so  that  we  know  clearly  what  we  have  first 
to  deny  if  we  do  not  wish  to  accept  it. 

The  divisions  of  hypothetical  reasoning  are 
Simple  and  Dilemmatic.  Simple  hypothetical  rea- 
soning is  further  divided  into  Constructive  and 
Destructive.  Dilemmatic  reasoning  is  also  divided 
into  Constructive  and  Destructive,  and  each  of  these 
into  Simple  and  Complex.  The  following  table  out- 
lines these  divisions  : 

/  ^-     ,  i        J Constructive. 
(  SlmP'e-  (Destructive. 

Hypothetical  Syllogisms  .A  .  Constructi  ve  i  Simple. 

(  Dilemmatic   1  Complex. 

1  Destructive]^. 

II.  SIMPLE  HYPOTHETICAL  SYLLOGISMS. 

— The  simple  hypothetical  syllogism  is  a  form  of 
reasoning  in  which  either  one  or  both  premises 
are  single  hypothetical  propositions.  Most  fre- 
quently it  is  the  major  premise  alone  that  is  con- 
ditional, while  the  minor  premise  and  conclusion 
are  thus  categorical.  The  proposition  called 
hypothetical,  and  regarded  as  single,  really  con- 
sists of  two  propositions,  one  of  which  is  depen- 
dent upon  the  other.  That  part  of  it  which  ex- 
presses the  condition  is  called  the  antecedent,  and 
that  part  which  depends  upon  their  condition  is 
called  the  consequent.  The  condition  is  indicated 
by  some  such  terms  as  if,  supposing,  granted  that, 
provided  that,  although,  had,  were,  etc.  The  con- 


140  LOGIC   AND    ARGUMENT 

sequent  has  no  sign.  But  an  illustration  of  the 
hypothetical  proposition  is  "  If  the  sea  is  rough,  it 
is  dangerous,"  of  which  the  first  part  is  the  ante- 
cedent, and  the  second  part  is  the  consequent. 

The  minor  premise  either  categorically  or  hypo- 
thetically  affirms  or  denies  one  or  the  other  of 
the  two  terms  in  the  major  premise,  and  as  this 
must  always  be  a  hypothetical  proposition,  antece- 
dent or  consequent  may  be  either  affirmed  or  de- 
nied. This  gives  four  forms,  or  Moods,  to  be 
considered,  two  of  which  are  valid  and  two  invalid 
modes  of  reasoning.  The  two  valid  Moods  are 
called  the  modus  ponens,  or  Constructive,  and  the 
modus  tollens,  or  Destructive  hypothetical  syllo- 
gisms. The  modus  ponens  means  that  if  the  an- 
tecedent be  affirmed  categorically  in  the  minor 
premise,  the  consequent  must  be  affirmed  categori- 
cally, or  follows  as  a  categorical  conclusion.  The 
only  effect  of  a  hypothetical  minor  premise  is  to 
make  the  conclusion  hypothetical.  The  modus 
tollens  means  that  if  the  consequent  be  denied,  the 
antecedent  must  be  denied.  The  two  forms  are 
illustrated  by  the  following  : 

Modus  Ponens. 

If  A  is  B,  C  is  D.        If  Iron  is  impure,  it  is  brittle. 

A  is  B.  or         Iron  is  impure. 

.-.  C  is  D.  .-.  Iron  is  brittle. 

Modus    Tollens. 

If  A  is  B,  C  is  D.      If  the  sun  shines,  it  is  light. 

C  is  not  D.     or     It  is  not  light. 
.-.  A  is  not  B.         .-.  The  sun  does  not  shine. 


HYPOTHETICAL    REASONING  14! 

The  rule,  therefore,  for  the  valid  forms  of  hy- 
pothetical reasoning  is  that  either  the  antecedent 
must  be  affirmed  or  the  consequent  denied.  The  gene- 
ral reason  for  this  will  appear  in  the  reduction  of 
hypothetical  syllogisms. 

The  two  false  Moods  are  illustrated  as  follows  : 

1st  Form. 

If  A  is  B,  C  is  D.        If  it  rains,  it  is  cloudy. 

C  is  D.  or         It  is  cloudy. 

..  A  is  B.  .-.  It  rains. 

2d  Form. 

If  A  is  B,  C  is  D.       If  Gold  were  cheap,  it  would 

be  useful. 

A  is  not  B.  Gold  not  cheap. 

•.  C  is  not  D.  .-.  Gold  is  not  useful. 

The  first  of  these  is  the  fallacy  of  affirming  the 
consequent,  and  the  second,  the  fallacy  of  denying 
the  antecedent.  The  general  rule  is  that  affirming 
the  consequent  or  denying  the  antecedent  causes  a  fal- 
lacy. The  reason  that  affirming  the  consequent 
leads  to  a  fallacy  is  the  fact  that  the  condition 
mentioned  in  the  major  premise  may  not  be  the 
only  one  determining  the  consequent.  Some  other 
condition  of  it  might  be  true  also,  and  affirming 
the  consequent  would  involve  this  also,  but  there 
is  no  way  of  determining  what  it  is.  It  might  be 
true,  for  instance,  that  "  If  it  is  not  raining,  it  is 
cloudy,"  and  if  affirmation  of  the  consequent  en- 
tailed the  antecedent,  we  could  as  well  conclude 


142  LOGIC   AND    ARGUMENT 

that  "It  is  not  raining,"  or  that  "  It  is  raining," 
two  contradictory  conclusions  from  the  same 
premise.  Hence,  we  have  no  right  to  draw  any 
inference  whatever.  A  concrete  illustration  will 
make  this  still  clearer.  If  a  man's  character  be  ava- 
ricious, he  will  refuse  to  give  money  for  charity  ; 
but  it  does  not  follow  that  every  person  who  re- 
fuses to  give  money  for  charity  is  avaricious,  as 
can  be  seen  by  the  impossibility  of  simple  con- 
version in  this  proposition.  There  may  be  many 
proper  reasons  other  than  avariciousness  leading 
him  to  refuse  ;  he  may  have  no  money,  he  may 
feel  that  it  would  do  more  harm  than  good,  or  he 
may  have  some  better  object  in  view.  No  infer- 
ence therefore  can  be  drawn  from  the  affirmation 
of  the  consequent. 

In  the  case  of  denying  the  antecedent  the  fal- 
lacy is  due  to  the  same  causes  as  in  the  first  case. 
The  antecedent  is  not  the  only  possible  condition 
of  the  consequent,  and  hence  the  denial  of  it  will 
not  prevent  the  consequent  from  being  a  fact  ex- 
isting by  virtue  of  dependence  upon  other  condi- 
tions. It  is  apparent  in  the  concrete  illustration 
given  that  other  qualities  besides  cheapness  might 
make  gold  useful,  and  therefore  the  absence  of 
this  quality  would  not  remove  the  usefulness  of 
the  metal. 

Difficulties  and  exceptions  to  this  dictum  appear 
in  many  cases,  such  as  : 

If  fire  is  hot,  it  will  burn. 
Fire  is  not  hot. 
.-.    It  will  not  burn. 


HYPOTHETICAL    REASONING  143 

But  in  such  instances  the  apparent  correctness 
of  the  reasoning  depends  upon  other  characteris- 
tics than  the  form  of  statement,  which  is  all  that 
formal  logic  can  recognize.  The  meaning  of  the 
major  premise  in  all  such  cases  is  either  that  of  a 
definition  making  subject  and  predicate  convert- 
ible, or  that  of  an  exclusive  proposition  making 
the  syllogism,  when  the  major  premise  is  convert- 
ed from  the  exclusive  to  a  universal  proposition, 
a  simple  modus  tollens,  one  denying  the  consequent. 
In  practical  reasoning,  therefore,  we  should  be  on 
the  alert  for  instances  which  appear  to  be  valid 
and  yet  appear  equally  to  violate  the  formal  rules, 
but  which  when  interpreted  rightly  conform  to 
them. 

One  important  observation  must  be  made  in 
order  to  determine  when  we  are  affirming  and 
when  denying  either  term  of  the  hypothetical 
proposition.  We  found  that  either  the  antecedent 
or  the  consequent,  or  both  antecedent  and  conse- 
quent may  be  negative,  as  : 

(a)  If  A  is  B,  C  is  not  D. 

(b)  If  A  is  not  B,  C  is  D. 

(c)  If  A  is  not  B,  C  is  not  D. 

In  all  such  cases  the  minor  premise  must  be 
negative  in  order  to  affirm,  and  affirmative  in 
order  to  deny  a  term,  antecedent  or  consequent, 
that  is  negative. 

III.  DILEMMATIC  REASONING.  —  The  di- 
lemma differs  from  the  simple  hypothetical  syllo- 
gism, not  in  the  form  of  reasoning,  but  only  in  the 
fact  that  either  the  minor  premise,  or  both  minor 


144  LOGIC    AND    ARGUMENT 

premise  and  the  conclusion  may  be  disjunctive 
propositions,  and  in  the  fact  that  the  major  pre- 
mise consists  of  two  hypothetical  propositions. 
The  first  form  of  it  is  the  simple  constructive  di- 
lemma : 

If  A  is  B,  C  is  D  ;  and  if  E  is  F,  C  is  D. 
Either  A  is  B,  or  E  is  F. 
.-.Cis  D. 

We  observe  in  this  and  all  similar  cases  that 
the  consequent  is  the  same  for  both  antecedents. 
This  gives  as  its  distinctive  mark  a  categorical  con- 
clusion. A  concrete  illustration  is  the  following  : 

"If  a  science  furnishes  useful  facts,  it  is  worthy 
of  being  cultivated  ;  and  if  the  study  of  it  exer- 
cises the  reasoning  powers,  it  is  worthy  of  being 
cultivated  ;  but  a  science  either  furnishes  useful 
facts,  or  its  study  exercises  the  reasoning  powers ; 
therefore  it  is  worthy  of  being  cultivated." 

The  second  form  is  the  complex  constrtictive  di- 
lemma : 

If  A  is  B,  C  is  D  ;  and  if  E  is  F,  G  is  H. 
Either  A  is  B,  or  E  is  F. 
.-.  Either  C  is  D,  or  G  is  H. 

In  this  instance  the  consequents  are  not  the 
same,  and  this  results  in  a  disjunctive  conclusion 
which  is  the  distinctive  mark  of  the  complex  con- 
structive dilemma.  The  following  is  a  concrete 
illustration  : 

"  If  a  statesman  who  sees  his  former  opinions 
to  be  wrong  does  not  alter  his  course,  he  is  guilty 
of  deceit ;  if  he  does  alter  his  course,  he  is  open 


HYPOTHETICAL    REASONING  145 

to  the  charge  of  inconsistency  ;  but  he  either 
does  not  alter  his  course,  or  he  does  alter  it  when 
he  remarks  a  change  of  opinions  ;  therefore  he  is 
either  guilty  of  deceit,  or  is  open  to  the  charge  of 
inconsistency." 

The  destructive  dilemma  also  takes  two  forms,  the 
simple  and  complex.  The  conclusion  is  again 
categorical  in  the  former  and  disjunctive  in  the 
latter.  The  following  is  the  form  of  the  simple 
destructive  dilemma  : 

If  A  is  B,  C  is  D  ;  and  if  E  is  F,  C  is  D. 
But  C  is  not  D. 
.-.  Neither  A  is  B,  nor  E  is  F. 

A  concrete  illustration  is :  "  If  it  rains,  the 
river  rises  ;  and  if  the  tide  flows,  the  river  rises  ; 
but  the  river  does  not  rise,  and  therefore  it  neither 
rains  nor  does  the  tide  flow." 

The  complex  destructive  dilemma  takes  the  fol- 
lowing form  : 

If  A  is  B,  C  is  D  ;  and  if  E  is  F,  G  is  H. 
Either  C  is  not  D,  or  G  is  not  H. 
.•.  Either  A  is  not  B,  or  E  is  not  F. 

The  concrete  example  is:  "If  this  man  were 
wise,  he  would  not  speak  irreverently  of  Scripture 
in  jest  ;  and  if  he  were  good,  he  would  not  speak 
irreverently  in  earnest ;  but  he  either  speaks  of 
it  irreverently  in  jest,  or  he  does  it  in  earnest ; 
therefore  he  is  either  not  wise,  or  not  good." 

The  fallacies  in  the  dilemma  are  the  same  as  in 
the  simple  hypothetical  syllogism,  and  arise  from 


146  LOGIC    AND    ARGUMENT 

the  attempt  to  draw  a  conclusion  after  affirming 
the  consequent  or  denying  the  antecedent. 

IV.  REDUCTION  OF  HYPOTHETICAL  TO 
CATEGORICAL  REASONING.  —  The  form  of 
statement  and  the  language  of  the  rules  in  hypo- 
thetical reasoning  do  not  betray  the  fact  that  it 
can  be  reduced  to  categorical  form,  but  this  is 
the  fact,  and  it  shows  a  simpler  conception  of  the 
general  process  than  might  be  imagined  from  the 
division  into  the  three  types.  It  enables  us  also 
to  see  the  Moods  and  Figures  in  categorical  syllo- 
gism to  which  the  Moods  of  the  hypothetical  syl- 
logism are  equivalent.  In  all  cases,  therefore,  of 
hypothetical  reasoning,  which  we  wish  to  reduce 
to  the  categorical  form,  we  have  only  to  regard 
the  antecedent  of  the  hypothetical  proposition  as  the 
subject  of  the  categorical,  and  the  consequent  of  the 
hypothetical  proposition  as  the  predicate  of  the  categor- 
ical. In  some  cases  this  change  is  a  very  simple 
one  ;  in  others  it  can  be  effected  only  by  a  circum- 
locution. The  following  is  an  illustration  of  this 
reduction  in  the  simpler  form  : 

Hypothetical. 

If  iron  is  impure,  it  is  brittle. 
Iron  is  impure. 
.'.  Iron  is  brittle. 

Categorical. 

Impure  iron  is  brittle. 
Iron  is  impure. 
/.  Iron  is  brittle. 


HYPOTHETICAL    REASONING  147 

Where  we  have  to  supply  a  circumlocution,  such 
phrases  as  "  the  case  of"  or  "the  circumstances  that' 
must  be  used,  as  in  the  following  instance  : 

Hypothetical. 

If   Aristotle    is    right,    slavery   is   a   legitimate 

institution. 

Slavery  is  not  legitimate. 
.•.  Aristotle  is  not  right. 

Categorical. 

The  case  of  Aristotle  being  right  on  slavery  is  a 
case  of  slavery  being  a  legitimate  institution. 
Slavery  is  not  legitimate. 
.*.  Slavery  is  a  case  of  Aristotle  not  being  right. 

If  now  we  look  at  the  first  instance  of  the  hypo- 
thetical syllogism  reduced  to  the  categorical,  we 
shall  discover  that  it  is  equivalent  to  AAA  of  the 
First  Figure  in  the  categorical.  This  is  a  case  of 
affirming  the  antecedent  and  is  valid,  as  also  AAA 
of  the  First  Figure  always  is.  But  if  we  affirm  the 
consequent  in  any  case  we  affirm  the  predicate  of 
the  categorical  proposition,  according  to  the  rule 
for  the  reduction,  and  hence  we  obtain  AAA  of 
the  Second  Figure  in  the  categorical  syllogism, 
which  is  an  error  of  illicit  or  undistributed  middle. 
But  if  in  the  minor  premise  we  deny  the  ante- 
cedent, we  have  a  case  of  AEE  of  the  First  Figure, 
which,  as  we  have  before  seen,  is  a  fallacy  of  illicit 
major.  If  we  deny  the  consequent,  we  have  a  case  of 
AEE  of  the  Second  Figure,  which  is  valid.  Hence, 


148  LOGIC   AND    ARGUMENT 

when  the  four  forms  of  hypothetical  syllogism  are 
reduced  to  the  categorical,  assuming  the  major 
premise  to  be  affirmative,  we  have  four  Moods  in 
the  categorical  syllogism  representing  the  reason- 
ing in  the  hypothetical.  These  are  AAA,  affirm- 
ative Moods,  of  the  both  Figures,  and  AEE,  neg- 
ative Moods,  of  the  both  Figures,  only  one  in 
each  case  being  valid.  If  the  maj,or  premise  of 
the  hypothetical  syllogism  be  n-egative,  we  may 
also  have  the  forms  EAE  of  both  the  First  and 
Second  Figures.  If  the  minor  premise  be  particu- 
lar, according  as  it  is  affirmative  or  negative,  we 
may  have  the  Moods  All,  AOO,  and  EIO  of  both 
Figures. 


CHAPTER   XI 
DISJUNCTIVE    REASONING 

I.  NATURE  OF  DISJUNCTIVE  REASONING. 

— A  disjunctive  syllogism  is  one  which  is  deter- 
mined by  the  presence  of  a  disjunctive  proposition 
in  the  major  premise,  and  in  the  conclusion  also 
when  the  disjunction  in  the  major  premise  con- 
tains more  than  two  terms.  A  disjunctive  propo- 
sition we  have  already  learned  to  be  one  which 
contains  alternative  predicates  for  the  subject  in 
which  either  and  or  are  used  to  denote  a  choice 
between  two  terms.  Wherever  "either — or "  is 
found  in  such  propositions,  the  expression  means 
that  only  one  of  two  things  can  be  affirmed  of  the 
subject,  and  that  the  other  or  others  must  be  de- 
nied. Thus,  when  we  say  that  "  The  weather  is 
either  clear  or  cloudy,"  we  mean  that  it  is  one,  it 
cannot  be  the  other.  It  is  this  kind  of  propo- 
sition that  determines  the  nature  of  the  disjunc- 
tive syllogism  and  the  manner  of  drawing  its  in- 
ferences. 

But  there  is  an  ambiguity  in  the  use  of  the  ex- 
pression "  either — or."  One  of  these  uses  implies 
a  contradiction  or  mutual  exclusion  between  the 
terms  of  the  disjunction.  This  is  the  proper  log- 
ical use  of  the  expression  in  defining  disjunctive 
149 


150  LOGIC   AND    ARGUMENT 

propositions.  The  second  meaning  of  the  expres- 
sion is  that  either  term  of  the  apparent  disjunction 
may  have  an  affirmative  connection  with  the  subject 
without  implying  that  the  other  is  negative,  or  that 
at  least  one  of  them  is  true,  though  both  may  be. 
This  is  illustrated  in  the  proposition,  "  Gibbon 
was  either  very  talented  or  very  industrious." 
Here  we  mean  that  at  least  one  of  these  qualities 
must  be  present  in  the  subject,  in  order  to  explain 
certain  facts.  Such  cases,  however,  are  not  true 
disjunctive  propositions,  as  they  have  to  be  con- 
ceived for  disjunctive  reasoning.  They  give  rise 
to  what  is  called  the  fallacy  of  incomplete  disjunction, 
a  form  of  petitio principii,  or  begging  the  question, 
considered  from  the  point  of  view  of  correct  dis- 
junctive propositions.  The  true  disjunctive  prop- 
osition must  use  "  either — or"  to  denote  reciprocal 
exclusion  between  their  predicates.  The  proper 
way,  therefore,  to  test  whether  a  proposition  is 
materially,  as  it  may  be  formally,  disjunctive  is  to 
convert  it  into  its  equivalent  hypothetical  propo- 
sitions, and  see  if  the  consequent  necessarily  fol- 
lows in  both  cases.  Thus,  in  the  proposition  "  A 
is  either  B  or  C,"  we  have  a  case  which  can  be  re- 
solved into  "  If  A  is  B,  it  is  not  C,"  and  "  If  A  is 
not  B,  it  is  C."  If  we  find  that  both  propositions 
are  true  in  this  result,  we  may  safely  assume  that 
the  disjunction  is  materially  what  it  is  formally. 
Otherwise,  while  the  formal  reasoning  may  be 
correct,  the  material  conclusion  may  be  false, 
owing  to  the  incomplete  disjunction  in  the  major 
premise.  There  is  no  formal  fallacy  in  disjunctive 
reasoning.  The  reason  for  this  will  be  seen  when 


DISJUNCTIVE    REASONING  151 

discussing  its  reduction  to  the  other  forms.  But 
one  important  fact  must  be  noted,  and  it  is  that 
when  we  say  "  A  is  either  B  or  C,"  we  mean  both 
"  if  A  is  B,  it  is  not  C  "  and  "  if  it  is  not  B,  it  is  C," 
etc.  This  brings  out  the  formal  exclusion  ex- 
pressed by  the  expression  "  either — or." 

II.  FORMS  OF  DISJUNCTIVE  REASONING. 
— There  are  two  forms  of  disjunctive  reasoning, 
called  the  modus  ponendo  fattens  and  the  modus  tollen- 
do  ponens.  The  meaning  of  the  first  is  that  if  we 
affirm  one  of  the  alternatives  we  must  deny  the  other, 
and  of  the  second,  that  if  we  deny  one  of  the  alter- 
natives we  must  affirm  the  other.  An  illustration  of 
each  is  the  following  : 

Modus  Ponendo  Tollens. 

A  is  either  B  or  C.  Oak  trees  are  either  tall 

or  short. 

A  is  B.  Oak  trees  are  tall. 

.*.  A  is  not  C.  .*.  Oak  trees  are  not  short 

If  we  said  "  A  is  C,"  the  conclusion  would  be 
"  A  is  not  B  ;  "  or  that  "  Oak  trees  are  short,"  it 
would  be  "  Oak  trees  are  not  tall." 

Modus   Tollendo  Ponens. 

A  is  either  B  or  C.  The  air  is  either  cool  or 

warm. 

A  is  not  B.  The  air  is  not  cool. 

.•.  A  is  C.  .'.  The  air  is  warm. 

The  case  of  incomplete  disjunction  can  be  illus- 
trated as  follows : 


152  LOGIC   AND    ARGUMENT 

Gibbon  either  had  great  talents  or  he  was  very 

industrious. 
He  had  great  talents. 
.*.  He  was  not  very  industrious. 

There  is  no  error  in  the  process  of  reasoning  in 
this  latter  instance,  but  only  in  the  assumption 
that  the  disjunction  in  the  major  premise  repre- 
sents a  contradiction  or  mutual  exclusion  between 
the  predicates. 

III.  REDUCTION  OF  DISJUNCTIVE  SYLLO- 
GISMS.— We  have  found  earlier  in  this  treatise 
that  a  disjunctive  proposition  is  categorical  in  its 
form,  but  hypothetical  in  its  meaning.  Proceed- 
ing upon  this  fact,  we  can  give  it  hypothetical  ex- 
pression, and  then,  if  need  be,  categorical  expres- 
sion without  disjunctive  form,  so  that  we  should 
have  but  one  set  of  principles  to  which  all  formal 
reasoning  can  be  reduced.  But  if  a  disjunctive 
proposition  can  be  reduced  to  a  hypothetical  one, 
as  the  alternative  predicates,  implying  the  connec- 
tion of  one  and  the  exclusion  of  the  other  from 
the  subject,  enables  us  to  do,  we  have  a  simple 
illustration  of  this  reduction  in  the  following  syl- 
logisms : 

Disjunctive.  Hypothetical. 

A  is  either  B  or  C.  If  A  is  B,  it  is  not  C. 

A  is  B.  A  is  B. 

/.  A  is  not  C.  /.  A  is  not  C. 

The  Moods  which  this  process  will  ultimately 
represent  will  depend  upon  whether  the  minor 


DISJUNCTIVE    REASONING  153 

premise  of  the  disjunctive  syllogism  be  affirmative 
or  negative,  or  whether  we  state  the  hypothetical 
equivalent  of  the  major  premise  in  an  affirmative 
or  negative  form.  This  can  be  worked  out  for 
each  case  without  illustration  here. 

One  peculiarity  in  the  disjunctive  syllogism 
makes  it  appear  to  violate  certain  rules  already  laid 
down  about  legitimate  reasoning.  We  notice  that 
in  disjunctive  syllogisms  we  may  have  a  negative 
conclusion  when  both  premises  are  affirmative, 
or  an  affirmative  conclusion  when  one  of  the  pre- 
mises is  negative.  This  is  shown  in  the  illustra- 
tions which  exhibit  the  two  forms  of  this  syllogism, 
where  there  is  a  negative  conclusion  in  the  modus 
Ponendo  tollens,  and  an  affirmative  one  in  the  modus 
tollendo  ponens.  But  this  exception  is  only  appar- 
ent. The  major  premise  of  a  disjunctive  syllo- 
gism actually  contains  or  implies  two  propositions 
when  we  come  to  state  its  meaning  ;  perhaps  even 
four.  "  A  is  either  B  or  C  "  means  that  "  If  A  is 
B,  it  is  not  C  ;"  that  "  If  A  is  not  B,  it  is  C  ;" 
that  "  If  A  is  C,  it  is  not  B  ;  "  and  that  "  If  A  is 
not  C,  it  is  B."  This  will  show  that  what  appears 
as  an  affirmative  proposition  really  implies  a  nega- 
tive by  virtue  of  the  contradiction  expressed  in 
the  disjunction,  and  the  implication  that  the  two 
or  more  predicates  cannot  be  affirmed  of  the  sub- 
ject at  the  same  time.  This  is  apparent  when  the 
major  premise  of  the  disjunctive  is  converted  into 
the  major  premise  of  the  hypothetical  syllogism. 
Here  if  the  form  "  A  is  either  B  or  C  "  is  reduced 
to  the  hypothetical  "  If  A  is  B,  it  is  not  C,"  we 
have  a  negative  proposition  for  the  major  premise 


154  LOGIC   AND    ARGUMENT 

of  the  hypothetical  syllogism,  and  its  categorical 
form,  so  that  the  modus  ponendo  tollens  of  the  dis- 
junctive will  become  the  modus  ponens  of  the  hypo- 
thetical, and  EAE  of  the  categorical  syllogism, 
which  gives  a  negative  proposition  for  its  conclu- 
sion. By  a  similar  process  we  could  explain  why 
it  seems  that  an  affirmative  conclusion  can  be 
drawn  when  one  of  the  premises  is  negative.  In 
this  we  see  that  the  modus  ponendo  tollens  of  the 
disjunctive  becomes  EAE  of  the  First  Figure  in 
the  categorical  syllogism,  and  the  modus  tollendo 
ponens  AAA  of  the  First  Figure  in  the  categori- 
cal. It  is  thus  the  complex  character  of  the  dis- 
junctive proposition  that  causes  the  apparent 
exception,  but  its  real  conformity  to  the  regular 
rule  for  reasoning. 


CHAPTER  XII 
FALLACIES 

I.  DEFINITION  AND  DIVISIONS The  term 

"  fallacy  "  is  derived  from  the  Latin  fallo,  denot- 
ing deception,  and  comes  to  mean  illusion,  or 
error.  But  in  Logic  "  fallacy "  must  be  dis- 
tinguished from  illusion,  in  its  psychological  sense. 
An  illusion,  even  perhaps  in  all  cases,  is  a  false 
interpretation  or  construction  of  the  data  of  sense- 
perception  ;  a  fallacy  is  an  error  in  reasoning. 
This  latter  term,  however,  is  often  applied  to 
those  errors  which  are  liable  to  occur  in  the  in- 
terpretation of  ambiguous  propositions,  made  so 
by  the  displacement  of  a  word  or  phrase,  or  by 
the  vocal  accent.  This  is  illustrated  in  the  so- 
called  semi-logical  fallacies  of  Accent  and  Amphi- 
bology, both  giving  rise  to  different  meanings  in  a 
proposition.  But  in  the  true  logical  sense  these 
errors  are  not  fallacies,  but  rhetorical  illusions. 
They  may  give  rise  to  fallacies  in  reasoning  by 
rendering  the  data  uncertain  and  equivocal,  but 
they  are  not  errors  in  the  reasoning  itself.  They 
are  simply  errors  of  interpretation  and  expres- 
sion. 

The  fallacies  with   which   logic  deals  may  be 
divided  into  Formal  and  Material,     They  are  all 
155 


156  LOGIC   AND    ARGUMENT 

errors  in  the  inference  or  transition  of  the  mind 
from  one  proposition  to  another.  But  a  formal 
fallacy  is  an  error  that  arises  from  a  violation  of 
the  formal  laws  of  the  syllogism.  It  is  incident 
to  the  form  or  statement  of  some  proposition  in 
relation  to  another,  or,  as  it  is  often  called,  a  fal- 
lacy in  dictione  or  in  voce.  It  arises  out  of  an  error 
in  the  distribution  of  terms  and  in  reasoning  from 
premises  forbidden  by  rules  six  and  nine.  On 
the  other  hand,  a  material  fallacy  is  one  which  is 
due  to  some  peculiarity  in  the  subject-matter  of 
the  reasoning,  and  hence  arises  independently  of 
the  form  of  statement ;  that  is,  independently  of  the 
quantity  and  quality  of  the  propositions,  and  so  is 
said  to  be  extra  dictionem.  The  formal  reasoning 
may  be  correct  enough,  but  owing  to  some  error 
in  the  material  elements  of  the  process  the  con- 
clusion may  be  vitiated,  as  in  the  ambiguity  of 
terms,  the  assumption  of  actually  false  premises, 
or  the  assumption  of  matter  not  found  in  the 
premises.  The  formal  fallacies  can  be  detected 
by  anyone  who  can  understand  merely  the  formal 
laws  of  reasoning,  but  material  fallacies  require 
that  the  reasoner  be  familiar  with  the  subject- 
matter  of  the  discourse  or  argument.  In  Political 
Economy,  for  instance,  anyone  familiar  with 
formal  reasoning  could  detect  formal  fallacies 
without  knowing  anything  about  the  subject  it- 
self, but  in  order  to  discover  material  fallacies 
he  must  know  enough  about  the  subject  and 
laws  of  Political  Economy  to  recognize  equivo- 
cal terms,  false  propositions  and  material  in  the 
conclusion  transcending  the  premises. 


FALLACIES  157 

II.  FORMAL  FALLACIES — Formal  fallacies 
have  been  sufficiently  defined  as  determined  by 
the  nature  of  the  premises  and  errors  in  distribu- 
tion. Their  classification  remains  to  be  briefly 
considered. 

i  st.  Illicit  Process  of  the  Middle  Term — 
This  fallacy  grows  out  of  the  failure  to  have  the 
middle  term  distributed  at  least  once  in  the  prem- 
ises. It  is  illustrated  as  follows  : 

Some  Pennsylvanians  are  Americans.  I    M    =  P 

All  Philadelphians  are  Pennsylvanians.        A    (s)  =  M 

.'.  Some  Philadelphians  are  Americans.  I      S    =  P 

2d.  Illicit   Process  of  the  Major  Term — The 

illicit  major  is  due  to  the  distribution  of  the  major 
term  in  the  conclusion  when  it  is  not  distributed 
in  the  premise.  Following  is  an  illustration  : 

All  men  are  carnivorous.  A       (M) =  P 

Some  animals  are  not  men.  O        S  x  (M) 

.  *.     Some  animals  are  not  carnivorous.  0         S  x  (P) 

3d.  Illicit  Process  of  the  Minor  Term — The 

illicit  minor  arises  from  the  distribution  of  the 
minor  term  in  the  conclusion  when  it  is  not  dis- 
tributed in  the  premise.  Following  is  an  illus- 
tration : 

No  Caucasians  are  negroes.  E       (M)  x  (p) 

All  Caucasians  are  mortal.  A        (M)  —  S 

No  mortals  are  negroes.  E       (5)  x  P 

4th.  Illicit  Process  with  Negative  Premises. — 
The  fallacy  in  this  instance  is  not  due  to  an  error 
in  the  distribution  of  terms,  but  to  the  attempt  to 


158  LOGIC    AND    ARGUMENT 

reason  to  what  is  not  implicitly  or  explicitly  in- 
cluded in  any  of  its  parts  in  the  premises.  Illicit 
distribution  is  a  partial  transgression  of  the  prem- 
ises quantitatively  considered,  while  the  present 
fallacy  is  a  total  transgression  of  them,  and  so  must 
be  illustrated  in  another  way  in  addition  to  the  ex- 
hibition of  distribution.  Following  is  an  illus- 
tration : 

No  men  are  quadrupeds.    E       (M)  x  (?) 
No  ruminants  are  men.      E        (M)  xf?) 


or 


FIG.  VIII. 

Either    one   of   the 
diagrams   in    this    in- 

i    i  stance    will    represent 

V  J  the  possible    relations 

^- of  subjects  and  predi- 
cates.     But  there  is 
nothing    specifically 
saidor  implied  thatwill 
enable  us  to  say  wheth- 
er    "ruminants"    are 
included    in   "  quadru- 
peds "  or  excluded  from  them.     Consequently,  we 
can  infer  neither  an  affirmative    nor   a   negative 
exclusion. 

5th.  Illicit  Process  with  Mixed  Premises  and 
Conclusions — This   is   the   fallacy  of   drawing  a 


FALLACIES 


'59 


negative  conclusion  from  affirmative  premises  and 
an  affirmative  conclusion  when  one  of  the  prem- 
ises is  negative.  The  mode  of  illustrating  it  or 
representing  it  by  diagrams  will  be  somewhat  sim- 
ilar to  that  of  negative  premises,  and  also  like  it  can- 
not be  represented  by  the  method  of  distribution. 

The  fallacy  of  particular  premises  and  that  of 
drawing  a  universal  conclusion  when  one  of  the 
premises  is  particular,  are  instances  of  illicit  dis- 
tribution of  terms  either  of  the  middle,  major, 
or  minor. 

III.  MATERIAL  FALLACIES — Material  fal- 
lacies have  been  defined  as  errors  growing  out  of 
the  subject-matter  of  the  conceptions  and  propo- 
sitions constituting  a  syllogism.  They  can  all  be 
reduced,  with  only  the  apparent  exception  of  the 
petitio  principii,  to  what  is  called  the  fallacy  of 
Quaternio  Terminorurn,  or  Four  Terms.  We  found 
in  one  of  the  rules  regulating  the  formation  of  the 
syllogism  that  it  must  have  three  and  only  three 
terms.  Four  terms  make  it  impossible  to  reason, 
because  they  introduce  matter  that  prevents  com- 
parison by  a  middle  term.  In  some  form  or  other 
all  the  material  fallacies  reduce  to  this  one  type  of 
four  terms.  This  introduction  of  new  matter  may 
be  either  in  the  premises  or  in  the  conclusion.  It 
may  be  introduced  into  the  premises  in  two  forms, 
and  into  the  conclusion  in  two  forms.  First,  the 
middle  term  may  have  a  different  meaning  in  each 
premise.  This  makes  it  equivocal  and  equivalent 
to  the  use  of  four  terms.  Second,  the  major  and 
minor  terms  may  each  or  either  of  them  have  a 
different  meaning  in  the  premise  from  that  in  the 


l6o  LOGIC   AND   ARGUMENT 

conclusion.  This  again  gives  a  double  significa- 
tion to  them,  which  is  equivalent  to  four  terms. 
But  this  form  of  four  terms,  which  is  due  to  a 
double  meaning  of  the  words,  may  be  called 
Equivocation,  the  first  class  of  material  fallacies. 
Third,  the  error  may  grow  out  of  assuming  a  prem- 
ise or  premises  which  may  be  false,  or  require  to 
be  proved.  Fourth,  we  may  assume  new  matter 
without  equivocation  in  the  conclusion  when  the 
premises  are  true  or  not  disputed.  In  both  of 
these  assumptions  we  take  something  for  granted, 
which  should  either  be  proved  or  shown  to  be  con- 
tained in  the  premises.  These  two  forms  of  fal- 
lacy may  be  called  Presumption,  as  indicating  some 
form  of  assumption  that  vitiates  the  conclusion, 
either  as  false  because  one  or  both  of  the  premises 
are  false,  or  as  not  contained  materially  within 
them.  The  two  general  material  fallacies,  there- 
fore, will  be  Equivocation  and  Presumption.  We 
shall  consider  them  in  their  order. 

i st.  Fallacies  of  Equivocation. — Fallacies  of 
Equivocation  are  due  to  the  use  of  ambiguous 
terms,  which  often  conceal  their  equivocal  mean- 
ing even  when  the  mind  sees  that  there  is  some- 
thing wrong  with  the  conclusion.  But  there  are 
two  forms  of  equivocation  which  are  based  upon 
a  certain  quantitative  import  in  terms  on  the  one 
hand,  and  a  certain  qualitative  import  on  the  other. 
One  of  these  deals  with  equivocations  between 
Collective  and  Distributive  terms  and  proposi- 
tions, and  the  other  with  equivocations  between 
Abstract  and  Concrete  terms  and  propositions. 
The  first  of  them  divides  into  Fallacies  of  Com- 


FALLACIES  l6l 

position  and  Division,  and  the  second  into  Fallacies 
of  Accident,  which  represent  three  specific  forms. 

i.  Composition  and  Division.  —  These  fallacies 
arise  from  the  confusion  of  collective  and  distribu- 
tive terms  or  propositions  with  each  other.  When 
the  major  premise  is  distributive  and  the  minor 
premise  collective,  the  fallacy  in  the  conclusion  is 
called  one  of  Composition.  When  the  major  prem- 
ise is  collective  and  the  minor  premise  is  distrib- 
utive, the  fallacy  is  one  of  Division.  To  put  the 
matter  in  another  form,  to  argue  from  a  distrib- 
utive to  a  collective  use  of  a  term  is  to  commit 
the  fallacy  of  composition  ;  to  argue  from  the 
collective  to  the  distributive  is  to  commit  the  fal- 
lacy of  division.  The  following  are  illustrations 
of  the  fallacy  of  Composition  : 

All  the  angles  of  a  triangle  are  less  than  two 
right  angles. 

A,  B,  C  together  are  the  angles  of  a  triangle. 
/.  A,  B,  C  together  are  less  than  two  right  angles. 

In  the  major  premise  of  this  syllogism  the  prop- 
osition is  true  if  taken  to  mean  that  each  angle  is 
less  than  two  right  angles,  but  we  have  attempted 
to  argue  from  this  truth  to  the  supposed  case  that 
the  same  angles  taken  together  are  less  than  two 
right  angles,  which  is  false.  A  similar  case  is  the 
following  : 

Thirteen  and  seventeen  are  prime  numbers. 
Thirty  is  thirteen  and  seventeen. 

.-.  Thirty  is  a  prime  number. 

In  the  major  premise  "  thirteen  "  and  "  seven- 
teen "  are  each  prime  numbers ;  in  the  minor 


1 62  LOGIC   AND    ARGUMENT 

premise  they  are  together  equal  to  thirty.  Hence, 
we  are  trying  to  argue  from  the  distributive  to 
the  collective  in  the  conclusion,  "  Thirty  is  a 
prime  number,"  which  is  false. 

Again,  if  we  were  to  argue  that,  because  "  All 
the  peers  derived  their  title  from  the  crown,"  and 
"  The  House  of  Parliament  consisted  of  all  the 
peers,"  therefore,  "  The  House  of  Parliament  de- 
rived its  title  from  the  crown,"  we  should  be  com- 
mitting the  fallacy  of  composition.  So  also  we 
cannot  argue  from  the  truth  of  the  individual  in- 
cidents of  a  story,  as  having  independently  oc- 
curred, to  the  truth  of  the  narrative  as  a  whole,  or 
collectively  taken. 

Illustrations  of  the  fallacy  of  Division  are  the 
following  : 

All  the  angles  of  a   triangle  are  equal  to   two 

right  angles. 

A  is  an  angle  of  a  triangle. 
.*.  A  is  equal  to  two  right  angles. 

In  this  instance  the  major  premise  is  true  col- 
lectively ;  that  is,  the  proposition  is  true  on  the 
assumption  that  the  phrase  "  All  the  angles " 
means  "All  the  angles  together."  But  the  minor 
premise  is  distributive,  and  hence  also  the  con- 
clusion, which  asserts,  falsely,  of  course,  what  is 
true  only  of  a  collective  term  in  the  major  prem- 
ise. Another  illustration  exhibits  the  same  fact : 

The  Germans  are  a  nation. 
Bismarck  and  Stein  are  Germans. 
.'.  Bismarck  and  Stein  are  a  nation. 


FALLACIES  163 

It  would  be  a  similar  fallacy  to  argue  from  the 
fact  that  Congress  had  voted  for  a  subsidy,  that 

Mr.  A ,  a  member  of  Congress,  had  voted  for 

it.  So  it  would  be  to  argue  that  every  individual 
house  made  a  city,  because  a  collection  of  them, 
including  these  individual  instances,  made  a  city. 
The  individual  items  of  expense  in  a  bill  need  not 
be  large  because  the  aggregate  is  large. 

2.  Fallacies  of  Accident. — The  fallacies  of  Acci- 
dent arise  from  equivocations  in  terms  expressing 
different  totals  of  attributes  or  qualities.  Here 
we  have  to  do  with  the  various  attribute  meanings 
of  conceptions.  For  instance,  the  term  "  chair  " 
means  now  a  piece  of  furniture,  and  again  the 
presiding  officer  of  an  assembly;  or  "paper"  is 
now  a  kind  of  substance,  and  again  the  sheets  of 
that  substance  used  for  printing  the  news.  Now  if 
we  argue  from  one  of  these  meanings  to  the  other, 
we  commit  some  kind  of  a  fallacy  of  Accident. 
This  term  comes  from  its  application  in  the  classi- 
fication of  ideas.  We  found  in  dealing  with  the 
predicables  and  with  Genus  and  Species  that  we 
required  certain  terms  to  express  the  common  and 
certain  terms  to  express  the  distinctive  qualities  of 
things.  These  were  conferentia  and  differentia. 
Essentia  or  Essence,  and  Accidentia  or  Accident, 
express  the  same  ideas.  Conferentia  denotes  the 
common  or  essential,  and  differential,  the  distin- 
guishing or  differential,  sometimes  the  accidental 
properties  of  things.  This  difference  in  the  mean- 
ing of  terms,  some  standing  for  only  conferentia 
or  common  properties,  making  them  abstract,  as  in 
all  general  abstract  terms,  and  others  standing  for 


164  LOGIC   AND    ARGUMENT 

both  the  conferentia  and  the  differentia,  making 
them  concrete,  as  in  all  singular  terms  and  the  ex- 
tensive use  of  general  terms — this  difference  often 
gives  rise  to  the  equivocal  use  of  certain  terms,  and 
a  confusion  of  their  abstract  with  their  concrete  use, 
or,  as  is  sometimes  said,  their  general  with  their 
particular  application.  Hence,  if  we  undertake  to 
argue  from  conferentia  or  essence  (abstract)  to 
differentia  or  accident  (concrete),  or  vice  versa, 
we  commit  some  fallacy  of  Accident.  This  takes 
three  forms  :  Simple  Accident,  Converse  Accident,  and 
Specific  Accident. 

(a)  Simple  Accident. — The  following  is  an  instance 
of  Simple  Accident  in  which  we  argue  from  what  is 
true  in  general  to  a  special  case.  It  is  a  very  old 
illustration  : 

What  you  bought  yesterday  you  eat  to-day. 
You  bought  raw  meat  yesterday. 
/.  You  eat  raw  meat  to-day. 

A  better  illustration  is  the  following,  in  which 
the  argument  is  from  the  abstract  to  the  concrete, 
or  from  what  is  true  of  the  essential  qualities  un- 
der certain  conditions,  to  what  is  supposed  to  be 
true  in  a  particular  form  and  without  these  con- 
ditions : 

Intoxicating  liquors  are  dangerous. 
A  glass  of  wine  is  an  intoxicating  liquor. 
/.  A  glass  of  wine  is  dangerous. 

Here  the  major  premise  represents  what  is  true, 
not  in  all  forms  and  quantities  of  liquor,  but  only 
in  regard  to  their  essential  characteristics,  while 


FALLACIES  165 

the  conclusion  asserts  the  same  predicate  of  a 
special  and  small  quantity  of  liquor.  In  both  in- 
stances the  argument  is  from  the  general  to  the 
special  case. 

(b)  Converse  Accident. — As  illustrations  of  Con- 
verse Accident  we  may  take  the  following  : 

Loyalty  to  the  government  is  the  duty  of  the 
citizen. 

Loyalty  to  Charles  I.  was  loyalty  to  the  govern- 
ment. 

.•.  Loyalty  to  Charles  I.  was  the  duty  of  the  citi- 
zen. 

Here  we  may  find  the  equivocation  either  in  the 
middle  or  the  minor  terms.  The  "  loyalty  to 
the  government"  may  be  of  different  kinds,  or 
the  "  loyalty  to  Charles  I."  may  be  different  in  the 
minor  premise  from  what  it  is  in  the  conclusion. 
The  latter  supposition  makes  the  case  clearer,  and 
we  find  that  it  represents  reasoning  from  the 
purely  personal  loyalty  of  the  minor  premise  to 
political  loyalty,  including  an  implied  personal 
loyalty  which  might  be  impossible  even  if  desired 
by  the  citizen.  Perhaps  a  better  illustration  is 
the  following  : 

Grape  juice  does  not  intoxicate. 
Wine  is  grape  juice. 
/.  Wine  does  not  intoxicate. 

Here  we  plainly  argue  from  the  special  form  of 
"grape  juice  "to  a  more  general  form  in  which 
only  the  essential  qualities  of  the  original  are  to 
be  found.  It  would  be  a  similar  fallacy  to  argue 


1 66  LOGIC   AND    ARGUMENT 

from  the  contemptible  character  of  one  reformer 
in  a  particular  cause  to  the  conclusion  that  all  re- 
formers are  bad. 

(c)  Specific  Accident. — The  case  of  Specific  Acci- 
dent is  illustrated  by  the  following  syllogism  in 
which  the  meaning  of  the  terms  that  are  equivocal 
represents  the  difference  between  two  species  rather 
than  the  difference  between  genus  and  species,  or 
vice  versa  : 

The  end  of  life  is  its  perfection. 
Death  is  the  end  of  life. 
.-.  Death  is  its  perfection. 

The  term  "end  "  is  used  in  this  instance  with  two 
distinct  meanings,  one  of  them  denoting  a  terminus, 
and  the  other  a.  purpose,  though  both  are  expressed 
by  the  same  sound.  This  is  simple  equivocation, 
and  has  usually  been  called  the  fallacy  of  Ambig- 
uous Middle,  but  it  can  be  ranked  with  those  of 
accident  by  remembering  that  we  argue  in  it  from 
one  accident  in  a  term  to  another  accident  in  the 
same  term.  This  will  enable  us  also  to  see  that 
the  same  fallacy  is  possible  with  the  major  and 
minor  terms.  Another  illustration  of  the  same 
fallacy  is  the  following  : 

All  criminal  actions  are  punishable  by  law. 

Prosecutions  for  theft  are  criminal  actions. 

.-.  Prosecutions  for  theft  are  punishable  by  law. 

In  the  major  premise  "criminal  actions  "  means 
conduct  that  is  wrong  or  unjust,  and  in  the  minor 
premise  the  same  phrase  means  only  a  suit  at  law, 
which  is  not  necessarily  bad  conduct.  Hence, 


FALLACIES  l6j 

there  is  an  equivocation  in  the  argument,  which 
reasons  from  an  accident  of  the  term  in  one  case 
to  an  accident  of  a  different  kind  in  the  other. 

(d)  Rules  for  Fallacies  of  Accident. — The  sim- 
plest rules  for  the  detection  of  the  various  fallacies 
of  accident  may  be  formulated  as  follows,  when 
they  depend  upon  the  middle  term  : 


I  The  major  premi 

Simple  Accident  . .  •(  The  minor  premi 
I  The  conclusion  f 


The  major  premise  true  in  a  general  sense, 
ise  true  in  a  specific  sense, 
false. 

1  The  major  premise  true  in  a  specific  sense. 
Converse  Accident  •<  The  minor  premise  true  in  a  generic  sense. 
|  The  conclusion  false. 

("The  major   premise  true  in   any  sense  different  from 
|      the  minor. 
Specific  Accident. .  -j  The  minor  premise  true  in  any  sense  different  from  the 

major. 
I  The  conclusion  false. 


When  the  fallacy  turns  upon  the  minor  and  major 
terms,  the  rules  have  to  be  expressed  in  a  slightly 
different  form. 

Simple  Accident  =  Substitution  in  the  conclu- 
sion of  a  specific  minor  or 
major  that  is  general  in 
the  premise. 

Converse  Accident  =  Substitution  in  the  conclu- 
sion of  a  general  minor  or 
major  that  is  specific  in 
the  premise. 

Specific  Accident  =  Substitution  in  the  conclu- 
sion of  one  specific  minor 
or  major  for  another  spe- 
cific meaning  of  the  same 
term  in  the  premise. 


l68  LOGIC   AND    ARGUMENT 

zd.  Fallacies  of  Presumption.  —  Fallacies  of 
Presumption,  as  already  defined,  are  those  of  either 
taking  something  for  granted  in  the  premises 
which  ought  to  be  proved,  or  of  assuming  new 
and  irrelevant  matter  in  the  conclusion.  They 
may  accordingly  be  divided  into  two  kinds  :  the 
Petitio  Principii,  or  Assumption  of  the  Principle, 
and  the  Fallacia  Consequents,  or  Inconsequence  ; 
also  generally  called  Non  Sequitur.  The  former 
is  usually  charged  when,  the  formal  reasoning 
being  correct,  the  conclusion  is  seen  to  follow 
from  the  premises,  but  is  not  accepted  because 
one  or  both  of  the  premises  are  denied  ;  the  latter 
is  charged  when  the  premises  are  admissible,  and, 
the  formal  reasoning  being  correct,  the  conclu- 
sion is  seen  to  be  either  false  or  not  included  in 
them. 

i.  Petitio  Principii. — The  common  name  for  this 
is  Begging  the  Question,  but  it  is  here  called  As- 
sumption of  the  Principle  or  general  truth  which 
is  used  for  proof.  It  means  that  the  proposition 
to  be  proved  is  in  some  way  simply  assumed  with- 
out proof.  We  divide  it  into  two  forms,  the  Peti- 
tio Argumenti,  or  Begging  the  Question,  and 
Ignoratio  Elenchi,  or  Evading  the  Issue.  Each  of 
these  is  divisible  into  two  forms,  and  will  be  dis- 
cussed in  the  proper  place. 

(a)  Petitio  Argumenti. — This  is  here  technically 
called  Begging  the  Question,  and  means  that  the 
proof  of  any  proposition  is  so  assumed  as  to  in- 
clude the  proposition  under  dispute.  This  as- 
sumption may  be  of  a  proposition  more  general 
than  the  conclusion,  or  really  identical  with  it. 


FALLACIES  169 

This  circumstance  gives  rise  to  two  forms  of  the 
Petitio  Argumenti ;  namely,  the  assumptio  non  pro- 
bata,  and  the  circulus  in probando. 

The  assumptio  nonprobata  occurs  when  the  prop- 
osition or  propositions  assumed  to  prove  a  given 
assertion  can  be  questioned  by  those  whom  we 
may  be  endeavoring  to  convince.  Suppose,  for 
instance,  that  we  have  asserted  the  proposition 
that  "  Church  and  State  should  be  united,"  and 
we  were  asked  to  prove  it.  To  satisfy  this  de- 
mand we  should  be  obliged  to  find  a  major  and 
minor  premise,  or  a  series  of  arguments,  in  which 
the  asserted  proposition  is  included  as  a  conclu- 
sion. The  syllogism  summarizing  the  process 
would  stand  as  follows  : 

Good  institutions  should  be  united. 
Church  and  State  are  good  institutions. 
.•.  Church  and  State  should  be  united. 

In  this  argument,  if  the  minor  premise  be  ad- 
mitted and  no  formal  fallacy  chargeable,  there  is 
no  way  to  escape  the  conclusion  but  to  deny  the 
truth  or  the  universality  of  the  major  premise, 
thus  implying  that  the  question  is  begged  or  as- 
sumed in  the  effort  to  prove  it.  It  might  be  true 
that  most  good  institutions  should  be  united,  but 
the  exception  of  "church  and  state"  might  be  the 
very  instance  that  prevents  my  right  to  assume  a 
universal  major  premise  containing  it. 

It  is  not  merely  the  failure  to  prove  one's  prem- 
ises that  constitutes  the  fallacy  of  begging  the 
question.  This  failure  must  be  one  which  occurs 
when  proof  is  needed  or  demanded,  and  this  is 


lyo  LOGIC   AND    ARGUMENT 

when  the  premise  in  turn  is  treated  as  a  conclu- 
sion to  another  argument.  Hence,  the  begging  of 
the  question  occurs  only  when  the  attempt  to 
prove  a  proposition  involves  the  assumption  of  it 
in  a  premise  that  the  hearer  or  opponent  does  not 
admit.  It  is,  perhaps,  most  frequent  when  trying 
to  convince  another  of  a  given  assertion,  although 
it  may  also  occur  whenever  we  are  trying  to 
prove  to  our  own  minds  a  conclusion  without  as- 
suring ourselves  sufficiently  of  the  stability  of  the 
premises  upon  which  the  conclusion  rests.  But  it 
is  most  frequent  in  arguments  with  others,  be- 
cause the  one  condition  of  proof  or  conviction  in 
such  cases  is  that  the  opponent,  reader,  or  friend 
admit  the  principle  upon  which  the  conclusion  is 
to  be  established,  while  the  subject  himself  may 
not  require  proof  at  all  for  his  conviction,  as  he 
already  accepts  the  proposition.  But  we  cannot 
prove  to  another  a  truth  with  premises  that  he  does 
not  admit.  He  simply  charges  begging  the  ques- 
tion because  he  is  not  obliged  to  admit  in  the  con- 
clusion what  he  does  not  admit  in  the  premises. 

Moreover,  a  proposition  in  the  conclusion  may 
be  true,  and  yet  not  be  proved  by  the  premises. 
The  advantage  of  proving  any  proposition  lies  in 
making  it  a  special  case  included  under  a  general 
law  or  class  of  unquestioned  character,  so  that 
when  a  person  has  admitted  the  larger,  he  must 
perforce  admit  the  smaller.  But  there  are  in- 
stances in  which  we  may  dispute  the  universality 
of  a  principle  or  premise  either  to  show  that  the 
conclusion  may,  so  far  as  we  know,  be  an  excep- 
tion, or  to  assert  that  it  has  not  been  proved  by 


FALLACIES  iyi 

such  a  process,  however  true  the  proposition  to 
be  proved  may  be  in  reality.  This  means  that  we 
may  even  charge  a  begging  of  the  question  when 
we  admit  the  conclusion,  if  the  premise  does  not 
contain  it,'  and  can  be  disputed.  Suppose  we  as- 
sert that  "  All  cattle  have  cloven  feet,"  and  are 
asked  to  prove  it.  The  syllogism  purporting  to 
meet  this  demand  may  stand  as  follows  : 

All  ruminants  are  cloven-footed. 
All  cattle  are  ruminants. 
/.  All  cattle  are  cloven-footed. 

Now,  though  we  admit  the  last  proposition  to  be 
true  as  a  matter  of  fact,  yet  we  can  say  that  it  is 
not  proved,  and  the  question  is  begged  by  the 
major  premise,  if  this  is  not  universally  true,  but 
is  assumed  to  be  so  for  the  sake  of  the  argument. 
It  is  one  thing  to  perceive  the  truth  of  a  propo- 
sition, and  it  is  another  to  prove  it  by  a  superior 
premise  or  condition.  The  charge  of  begging  of  the 
question,  then,  may  be  made,  not  only  when  the  con- 
clusion is  denied,  but  also  when  it  is  not  proved. 

The  circulus  in  probando  is  a  species  of  begging 
the  question  which  consists  of  what  is  called 
"arguing  in  a  circle,"  or  in  assuming  as  proof  of  a 
proposition  that  proposition  itself.  Thus,  it  would 
be  arguing  in  a  circle  to  say  that  "  Man  is  wise 
because  he  is  intelligent  and  prudent  ;  "  for  "  in- 
telligence and  prudence  "  are  considered  the  same 
as  "  wisdom."  So  also  would  it  be  to  argue  that 
the  "Weather  is  warm,  because  it  is  summer,  and 
it  is  summer,  because  the  weather  is  warm,"  and 
"  Men  never  practise  excess,  because  they  are  not 


172  LOGIC   AND    ARGUMENT 

guilty  of  immoderate  habits."  Jevons  gives  the 
following  illustration  :  "  Consciousness  must  be 
immediate  cognition  of  an  object ;  for  I  cannot 
be  said  really  to  know  a  thing  unless  my  mind  has 
been  affected  by  the  thing  itself."  Here  "  to  know  " 
and  "  immediate  cognition  "  are  identical  in  mean- 
ing and  cannot  be  used  to  prove  each  other.  The 
difference  between  this  fallacy  and  the  assumptio 
non  probata,  as  explained  and  illustrated,  is  that 
the  "  circulus  in  probando"  assumes  an  identical 
proposition  as  proof,  while  the  former  assumes  a 
more  general  one  including  or  intending  to  include 
the  conclusion. 

The  fallacy  of  reasoning  in  a  circle  occurs 
mostly  in  long  arguments  where  it  can  be  commit- 
ted without  ready  detection.  In  such  cases  as  are 
given  above,  the  fallacy  is  perfectly  obvious.  But 
when  it  occurs  in  a  long  discourse  it  may  be  com- 
mitted without  easy  discovery.  It  is  likely  to  be 
occasioned  by  the  use  of  synonyms  which  are 
taken  to  express  more  than  the  conception  involved 
when  they  really  do  not.  It  is  difficult  to  give 
any  formal  expression  to  this  circumstance  with- 
out resorting  to  complex  syllogisms  for  examples. 
But  if  in  the  following  case  A  and  C  are  really 
identical  in  meaning,  though  apparently  not  so, 
we  shall  have  a  circulus  in  probando. 

A  is  B.  Bimana  are  rational. 

C  is  A.  Men  are  bimana. 

.'.  C  is  B.         .-.  Men-are  rational. 

Usually,  however,  the  form  is  much  more  likely 
to  take  the  form  of  a  prosyllogism  and  an  episyl- 


FALLACIES  173 

logism  in  which  we  arrive  at  some  proposition  for 
proof  which  is  absolutely  identical  with  the  propo- 
sition to  be  proved.  The  following  example  illus- 
trates this  fact : 

C  is  B.  The  months  of  the  earth's  aphelion 

are  warm. 

A  is  C.  The  season  from  June  to  Septem- 

ber is  the  months  of  the  earth's 
aphelion. 

.•.  A  is  B.  The  season  from  June  to  Septem- 

ber is  warm. 

C  is  A.  Summer  is  the  season  from  June 

to  September. 
/.  C  is  B.         .-.  Summer  is  warm. 

Here  the  term  "  summer  "  and  "  the  months  of 
the  earth's  aphelion  "  are  absolutely  identical  in 
meaning,  though  concealed  in  the  terms  by  which 
the  propositions  are  expressed.  It  is  therefore  a 
case  of  reasoning  in  a  circle. 

(b)  Ignoratio  Elenchi. — This  fallacy  is  properly 
defined  as  an  evasion  of  the  issue.  It  is  sometimes 
called  irrelevant  conclusion,  but  this  is  equally  ap- 
plicable to  the  non  sequitur,  while  the  ignoratio 
elenchi  is  more  properly  an  evasion  of  the  issue, 
or  a  disregarding  of  the  question  to  be  proved. 
It  also  takes  two  forms,  which  are  :  Evasio  ad  Dic- 
tionem,  or  Evasion  of  Proof,  and  Evasio  ad  Contra- 
dictionem  or  Evasion  of  the  Disproof. 

The  evasio  dictionem  is  committed  when  we  un- 
dertake to  prove  a  proposition  which  we  falsely 
assume  to  be  identical  with  the  real  proposition  at 
issue.  Thus,  if  we  announce  the  issue  to  be  that 


174  LOGIC   AND    ARGUMENT 

"Church  and  State  should  be  united,"  and  prove 
only  that  "  Church  and  State  are  good  institu- 
tions," we  have  evaded  the  issue.  An  illustration 
of  the  process  and  of  the  manner  in  which  the 
evasion  is  committed  is  the  following  : 

Ad  rent. 

Good  institutions  should  be  united. 
Church  and  State  are  good  institutions. 
.-.  Church  and  State  should  be  united. 

Non  ad  rem. 

Social  organizations  are  good  institutions. 
Church  and  State  are  social  organizations. 
.-.Church  and  State  are  good  institutions. 

The  error  in  this  instance  lies  in  the  assumption 
that  the  proof  of  the  proposition  "  Church  and 
State  are  good  institutions "  includes  also  the 
proposition  "  Church  and  State  should  be  united." 

There  are  several  forms  of  this  evasion  which 
are  legitimate  for  the  purpose  of  convincing  an 
opponent  or  the  persons  to  whom  we  are  appeal- 
ing, but  which  are  nevertheless  not  arguments 
directed  to  the  issue  by  itself,  and  hence  are 
treated  as  evasions  of  the  question.  The  argu- 
ment directed  correctly  to  the  issue  is  called  the 
argumentum  ad  rem.  The  reasoning  which  ignores 
it,  which  I  shall  call  the  argumentum  ad  personam 
and  which  nevertheless  may  be  useful  for  influ- 
encing an  opponent,  is  divided  into  five  forms  : 
the  argumentum  ad  judicium,  argumentum  ad  popu- 
lum,  argumentum  ad  hominem,  argumentum  ad  vere- 
cundiam,  and  argumentum  ad  ignorantiam.  These 
may  be  briefly  defined  and  illustrated. 


FALLACIES 


175 


The  argumentum  ad  judicium  is  an  appeal  to 
general  or  universal  consent  and  is  consequently 
based  upon  the  common  judgments  of  mankind. 
It  is  used  to  establish  a  case  where  we  suppose 
difficulties  in  getting  facts  to  support  the  real 
issue.  Thus,  if  we  are  asked  to  prove  the  exist- 
ence of  matter,  the  merits  of  democracy,  or  the 
truth  of  Ptolemaic  astronomy,  we  may  appeal  to 
the  universal  belief  of  mankind  as  the  ground 
upon  which  these  convictions  rest.  The  major 
premise  would  be  "Whatever  universal  consent 
attests  is  true,"  etc.,  and  the  minor  premise  would 
be  the  conformity  of  the  special  case  to  this  con- 
dition, and  hence  the  conclusion.  But  it  evades 
the  issue  because  the  question  is  not  what  men 
believe  in  the  premises,  but  what  the  facts  are. 

The  argumentum  ad  populum  is  an  appeal  to 
public  opinion,  or  to  the  passions  and  prejudices 
of  the  people  rather  than  to  their  intelligence. 
Thus,  if  the  issue  be  the  justice  of  protection  or 
free  trade,  we  may  appeal  to  the  interests  and 
political  passions  of  men  rather  than  to  reason 
and  fact. 

The  argumentum  ad  hominem  is  an  appeal  to  the 
practice,  profession,  or  principles  of  the  person  to 
whom  or  against  whom  an  argument  is  directed. 
It  is  an  effective  method  of  silencing  an  opponent, 
but  it  is  not  an  ad  rem  argument  and  does  not 
prove  the  issue. 

The  argumentum  ad  verecundiam  is  an  appeal  to 
authority,  or  body  of  accepted  doctrines.  It  is 
valid  for  producing  conviction  when  the  author- 
ity is  accepted  by  the  persons  to  whom  the  appeal 


176  LOGIC   AND    ARGUMENT 

is  addressed,  but  it  is  not  ad  rem  proof,  and  when 
not  accepted  by  anyone  is  still  more  glaring  as  an 
ignoratio  clenchi. 

The  argument  ad  ignorantiam  is  an  appeal  to  a 
man's  ignorance  in  order  to  produce  conviction 
upon  the  ground  of  his  inability  to  dispute  the  case. 

These  several  forms  of  argumenta  are  essen- 
tially the  same  in  their  principles  and  import,  and 
though  they  do  not  accomplish  real  proof,  and  to 
that  extent  evade  the  issue,  yet  they  have  the 
legitimate  use  of  driving  a  man  to  define  his 
position  and  to  clear  up  the  implied  contradictions 
involved  in  the  application  of  the  ad  hominem 
argument  against  him.  An  excellent  illustration 
of  both  the  legitimate  and  the  illegitimate  use  of 
this  form  of  argument  is  found  in  the  story  of 
Zeno  and  his  argument  against  the  possibility  of 
motion.  He  maintained  that,  if  motion  be  pos- 
sible, a  body  must  move  either  where  it  is  or 
where  it  is  not.  He  said  that  it  could  not  move 
where  it  is,  because  it  must  be  at  rest  to  be  in  any 
given  point.  Then  it  could  not  move  where  it  is 
not,  because  it  is  not  there  to  move.  Therefore, 
it  could  not  move  at  all.  Tradition  has  it,  says 
De  Morgan,  that  Zeno  called  in  a  physician  to  set 
a  dislocated  shoulder,  and  the  physician  badgered 
the  patient  by  turning  his  argument  about  motion 
upon  the  philosopher  to  prove  that  his  shoulder 
was  not  hurt.  He  argued  that  the  shoulder  must 
be  put  out  of  its  place  either  where  it  was  or 
where  it  was  not,  etc.  This  is  an  excellent  case 
of  the  ad  hominem  appeal.  It  admirably  exposes 
the  philosopher's  plight  in  his  contention  about 


FALLACIES  177 

motion,  but  it  neither  proves  nor  disproves  the 
possibility  of  motion.  Nor  is  it  a  refutation  of 
the  assertion  which  is  imputed  in  the  story  that 
the  philosopher's  shoulder  was  out  of  place.  It 
only  establishes  a  contradiction  between  his  phil- 
osophic denial  of  motion  and  his  present  belief 
about  the  dislocation  of  his  shoulder,  a  belief 
which  implied  the  assertion  of  motion.  The  philos- 
opher would  only  have  to  say  either  that  this  was 
not  a  case  of  motion,  or  that  his  shoulder  was  not 
displaced  in  order  to  recover  his  consistency  and 
to  indicate  that  his  argument  was  not  overthrown, 
while  admitting  that  the  physician's  reasoning  was 
correct.  But  he  would  have  to  yield  something, 
hence  he  must  either  explain  the  contradiction  or 
give  up  one  of  the  alternatives.  This  is  the  value 
of  the  ad  hominem  argument. 

The  second  form  of  the  ignoratio  clenchi,  name- 
ly, the  evasio  contradictionis,  remains  to  be  consid- 
ered. This  means  the  evasion  of  the  contradiction 
or  disproof  of  an  assertion.  An  illustration  of 
this  evasion  is  the  following :  Suppose  that  one 
man  asserts  that  "  A  is  not  a  thief,"  and  produces 
his  argument  therefor,  while  it  is  the  duty  of  an 
opponent  to  refute  this  assertion.  What  he  ought 
to  prove  is  that  "A  is  a  thief;  "  but  if  he  only 
proves  or  tries  to  prove  that  "A  is  a  rogue,"  he 
completely  evades  the  issue.  The  whole  case  is 
illustrated  as  follows  : 

Proof.  Disproof.  Ignoratio  Elenchi. 


.'.  A  is  not  a  thief.       .-.  A  is  a  thief.  .-.  A  is  a  rogue. 

12 


178  LOGIC    AND    ARGUMENT 

Here  the  opponent  assumes  that  if  he  can  only 
prove  that  "  A  is  a  rogue,"  he  has  won  his  case 
against  the  affirmative,  when,  in  fact,  he  assumes 
the  identity  between  this  and  the  proposition  "A 
is  a  thief,"  which  is  the  contradictory.  But  he 
thus  begs  the  question  while  he  evades  the  issue, 
which  is  not  that  "  A  is  not  a  rogue,"  but  that  "  A 
is  not  a  thief,"  "  rogue  "  and  "  thief "  being  differ- 
ent things,  so  that  he  might  be  a  rogue  and  yet 
not  a  thief. 

2.  Non  Sequitur. — The  fallacy  is  that  of  False 
Consequent.  It  arises  in  connection  with  the  con- 
clusion and  not  in  connection  with  the  premises. 
It  therefore  consists  in  the  introduction  of  new  mat- 
ter into  the  conclusion,  matter  that  is  not  contained 
in  the  premises.  There  is  no  special  necessity 
for  subdividing  it  into  distinct  forms,  except  that 
one  class  has  received  a  separate  name  for  the 
sake  of  particular  convenience,  and  perhaps  be- 
cause of  its  frequent  occurrence.  If  we  must 
distinguish  between  kinds  at  all,  which  could  be 
made  as  numerous  as  the  classes  of  everything,  it 
must  be  into  the  non  sequitur  simplex,  and  the 
non  causa,  pro  causa,  false  cause,  or  post  hoc  fallacy, 
whose  dictum  is  post  hoc,  ergo  propter  hoc.  The 
simplest  form  in  which  this  fallacy  may  occur  can 
be  illustrated  in  the  following  : 

All  men  are  rational. 
Socrates  is  a  man. 
.*.  Socrates  is  noble. 

It  is  evident  that  this  conclusion  cannot  follow 
from  the  premises.     The  major  term  is  not  "  no- 


FALLACIES  179 

ble,"  but  "  rational,"  and  hence  the  former  cannot 
follow.  De  Morgan  gives  a  good  illustration  that 
is  a  little  more  complex  : 

Episcopacy  is  of  Scripture  origin. 

The  Church  of  England  is  the  only  Episcopal 

church  in  England. 
.\  The  church  established  is  the  church  that  ought 

to  be  supported. 

Nothing  here  is  said  in  the  premises  about  "sup- 
porting the  church,"  and  hence  cannot  be  inferred 
in  the  conclusion.  This  non  sequitur  closely  re- 
sembles the  formal  fallacies  of  illicit  minor  and 
illicit  major,  but  a  wide  difference  nevertheless  is 
marked  in  the  fact  that  in  the  former  the  addition 
in  the  conclusion  is  new  quantity,  while  in  the  lat- 
ter it  is  new  quality  ;  that  is,  new  subject-matter. 

The  fallacy  of  False  Cause,  or  the  post  hoc  fal- 
lacy, is  the  most  important  form  of  non  sequitur  to 
be  considered.  It  consists  in  arguing/rom  a  mere 
co-existence  or  sequence,  a  coincidence  to  causal  or 
necessary  connection.  Thus,  to  argue  that  a  change 
of  weather  was  due  to  the  occurrence  of  a  new 
moon  because  they  coincided,  once  we  may  say, 
would  be  to  commit  this  fallacy ;  or  to  attrib- 
ute a  pestilence  to  the  appearance  of  a  comet,  a 
death  in  the  family  to  an  eclipse  of  the  sun,  good 
luck  to  carrying  a  bone  in  one's  pocket — all  these 
are  cases  of  confusing  cause  with  coincidence.  The 
phrase  post  hoc,  ergo  propter  hoc,  meaning  "  after 
a  fact,  therefore  because  of  it,"  describes  this 
fallacy  exactly.  If  we  have  observed  a  large 
number  of  such  coincidences  under  various  and 


180  LOGIC   AND    ARGUMENT 

changing  circumstances  and  conditions,  we  may 
be  justified  in  suspecting  a  causal  connection,  but 
the  coincidence  is  no  proof  of  it,  especially  if  it 
be  either  a  single  one  or  between  phenomena  that 
betray  no  intrinsic  characteristics  of  necessary 
connection.  This  latter  remark  is  true  of  even  con- 
stant co-existences  and  sequences.  We  cannot  in- 
fer that  night  is  the  cause  of  day  on  the  ground 
of  their  constant  conjunction.  The  idea  of  neces- 
sary or  causal  connection  is  not  contained  in  that 
of  merely  actual  connection,  and  it  is  a  non  scquitur 
to  include  this  new  matter  in  the  conclusion  when 
the  premises  express  nothing  more  than  co-exist- 
ence or  sequence.  Thus,  if  I  argue  from  the  coin- 
cidence between'  the  existence  of  a  protective  tariff 
and  the  fall  in  price  of  iron,  I  commit  this  fallacy, 
because  I  assume  that  there  are  no  other  possible 
causes  of  reduction  in  price.  Similarly  with  any 
other  such  coincidence  in  which  the  conclusion 
contains  new  and  different  matter  from  the  prem- 
ises. 

IV.  GENERAL  OBSERVATIONS.— It  is  im- 
portant to  remark  that  the  errors  in  reasoning  are 
capable  of  being  looked  at  from  different  points 
of  view,  and  hence  are  so  interconnected  that 
what  may  be  one  fallacy  in  one  interpretation  of 
the  premises  may  be  adjudged  a  different  fallacy 
with  another  interpretation  of  the  premises. 
Thus,  to  take  the  case  of  the  non  sequitur  which 
we  have  just  been  discussing,  we  may  reduce  it  in 
some  cases  to  a  petitio  principii.  For  instance,  we 
have  said  that  to  argue  from  the  sequence  of 
night  and  day  to  a  causal  connection  was  to  commit 


FALLACIES  l8l 

the  post  hoc  fallacy.  This  is  true  if  we  look  only  at 
the  material  difference  between  what  is  here  only 
a  minor  premise  and  the  conclusion.  But  being 
merely  an  enthymeme,  if  we  supply  the  major 
premise  we  have  : 

All  immediate  antecedents  of  day  are  its  cause. 
Night  is  the  immediate  antecedent  of  day. 
.*.  Night  is  the  cause  of  day. 

Here  if  the  major  premise  be  true  the  conclu- 
sion may  follow,  but  a  dispute  on  the  truth  of  this 
premise  reduces  the  argument  to  a  petitio  principii. 
Hence,  what  may  be  charged  as  a  non  sequitur  in 
relation  to  the  minor  premise,  may  be  viewed  as  a 
petitio  principii  in  relation  to  the  major  premise. 
This  will  always  be  true  of  enthymemes  when  we 
observe  that  the  conclusion  is  not  contained  in 
the  stated  premise. 

A  similar  reduction  can  be  made  of  the  falla- 
cies of  accident.  Take  the  following  example  : 

Pine  wood  is  good  for  lumber. 
Matches  are  pine  wood. 
.  Matches  are  good  for  lumber. 

Here  we  have  a  fallacy  of  Simple  Accident,  due 
to  arguing  from  the  general  to  the  special  case, 
or  from  the  abstract  to  the  concrete.  But  calling 
it  a  fallacy  of  accident  depends  upon  the  question 
whether  we  admit  the  premises  and  do  not  ad- 
mit the  conclusion.  We  may,  however,  question 
the  major  premise  in  this  case,  or  even  the 
minor.  We  are  tempted  to  admit  the  major  prem- 
ise because  we  know  that  "  pine  wood  is  good 


1 82  LOGIC    AND    ARGUMENT 

for  lumber,"  but  we  forget,  perhaps,  to  observe 
the  qualifications  under  which  it  is  true.  It 
should  be  noticed  that  the  statement  carefully 
omits  to  say  either  "  All  pine  wood,"  or  "  All 
forms  of  pine  wood,"  and  hence  expresses  what  is 
only  abstractly  true  ;  that  is,  true  of  "  pine  wood" 
as  a  substance,  and  seeing  this  we  may  not  notice 
the  trap  into  which  we  fall  until  the  conclusion  is 
announced,  which  is  palpably  false.  If  this  major 
premise  be  considered  as  universally  true  at  all,  it 
is  only  in  the  abstract  sense  that  the  quality  of 
pine  wood  fits  it  for  the  purpose  of  lumber,  but 
the  minor  premise  has  to  do  with  pine  wood  in  a 
special  concrete  form,  and  an  equivocation  arises 
which  we  may  call  a  fallacy  of  accident,  assuming 
that  formally  the  reasoning  is  correct. 

But  we  may  dispute  the  truth  of  the  major  pre- 
mise, if  we  like,  as  not  being  true  in  the  concrete 
sense  in  which  it  ought  to  be  true  if  the  argument 
is  to  be  valid,  and  hence  we  could  charge  the  fal- 
lacy of  begging  the  question  by  thus  raising  a  doubt 
about  the  first  condition  of  the  argument.  Again, 
we  may  maintain  that  the  proposition,  as  true,  is 
really  a  particular  proposition  ;  that,  taken  as 
true,  it  can  only  mean  "  Some  pine  wood  is  good 
for  lumber,"  and  in  this  interpretation  we  should 
have  IAA  of  the  First  Figure,  which  represents 
the  fallacy  of  illicit  middle.  Hence,  according  to 
the  way  we  look  at  the  propositions  in  this  in- 
stance, we  may  have  any  one  of  three  fallacies, 
simple  accident,  petitio  principii,  or  illicit  middle.  A 
similar  treatment  of  the  fallacies  of  Composition 
and  Division  could  be  made,  but  it  suffices  to 


FALLACIES  183 

show  what  the  principle  is  in  the  previous  in- 
stances. 

Another  important  remark  in  this  connection  is 
that  it  is  not  necessary  to  put  an  argument  into 
the  form  of  a  syllogism  in  all  cases  in  order  to 
discover  what  the  fallacy  is,  if  any.  We  have  only 
to  observe  the  quantity  of  the  propositions  serv- 
ing as  premises  and  conclusion,  the  relation  be- 
tween premises  and  conclusion,  and  the  manner  in 
which  one  term  is  substituted  for  another.  In 
actual  discourse  the  arguments  are  most  fre- 
quently expressed  either  in  the  form  of  enthy- 
memes,  or  in  a  manner  to  effectually  conceal  the 
syllogistic  figures  and  moods,  so  that  we  are  left 
entirely  to  depend  upon  the  resources  just  men- 
tioned for  the  detection  of  fallacies.  Moreover, 
since  the  construction  of  enthymemes  into  com- 
plete syllogisms  leaves  us  practically  free  to  put 
them  into  either  the  First  or  Second  Figures  at 
pleasure,  the  first  of  these  being  formally  valid 
in  nearly  all  cases  so  reconstructed,  we  have 
always  to  allow  for  this  as  the  possible  meaning 
of  the  debater,  and  so  look  for  material  fallacies 
if  we  refuse  to  accept  the  conclusion.  But  when 
any  doubt  exists  about  the  case,  the  only  recourse 
is  to  throw  the  argument  into  syllogistic  form. 

Another  important  observation  to  make  is  the 
fact  that  the  imputation  of  a  fallacy  in  the  reason- 
ing does  not  necessarily  imply  that  the  proposition 
in  the  conclusion  is  a  false  one.  The  fallacy  is 
not  a  reason  for  the  falsity  of  a  proposition,  but  is 
only  an  explanation  of  the  failure  to  prove  it.  In 
some  cases  the  reasoning  may  be  valid  and  the  con- 


184  LOGIC    AND    ARGUMENT 

elusion  false,  or  the  reasoning  fallacious  and  the 
conclusion  be  true,  as  a  proposition.  Reasoning 
avails  only,  when  valid,  to  show  the  connection  of 
the  conclusion  with  the  premises,  and  all  of  these 
may  be  either  true  or  false  without  affecting  the 
reasoning  process.  All  that  the  existence  of  a 
fallacy,  which  is  a  violation  of  the  rules  for  legiti- 
mate transition  from  term  to  term  or  proposition 
to  proposition,  can  establish  is  a  mistake  in  the 
mode  of  proving  a  statement,  not  the  truth  or 
falsity  of  it,  except  relative  to  the  same  quality 
in  the  premises.  It  is  the  perceived  falsity  of  a 
statement  that  often  leads  us  to  question  the 
validity  of  its  deduction,  but  we  cannot  suppose 
that  the  process  of  reasoning  determines  either 
the  truth  or  falsity  of  a  proposition.  It  only 
settles  whether  it  is  implied  by  the  premises,  and 
its  truth  stands  or  falls  with  the  same  character 
in  the  statements  from  which  the  deduction  is 
attempted. 


CHAPTER    XIII 
INDUCTIVE    REASONING 

I.  GENERAL  NATURE  OF  INDUCTIVE 
REASONING. — Inductive  inference  has  been  dis- 
tinguished from  deductive  reasoning  ever  since 
Logic  was  founded,  but  it  has  not  always  suc- 
ceeded in  keeping  its  meaning  perfectly  clear.  It 
is  important  therefore  that  we  should  briefly  ex- 
plain the  various  uses  of  the  term.  This  can  be 
done  by  assuming  the  two  divisions  of  Induction, 
which  are  commonly  accepted.  They  are  Perfect 
Induction  and  Imperfect  Induction. 

i st.  Perfect  Induction. — Perfect  Induction  is 
an  enumeration  of  the  particulars  that  form  a  class. 
It  is  the  process  which  characterized  the  method 
of  Socrates  in  reaching  definitions.  An  example 
of  it  is  the  following  :  Mercury  revolves  on  its 
axis  ;  so  do  Venus,  the  Earth,  Mars,  Jupiter, 
Saturn,  and  Neptune.  But  these  being  all  of  the 
planets,  we  can  say,  "All  the  planets  revolve  on 
their  axes."  This  appears  to  be  in  the  form  of 
reasoning,  but  in  reality  it  is  not  reasoning.  It 
should  be  called  simply  Generalization.  All  the 
individuals  that  constitute  the  class  are  simply 
enumerated,  so  that  the  generalized  expression  is 
but  an  economical  device  for  avoiding  the  specific 
185 


1 86  LOGIC    AND    ARGUMENT 

mention  of  the  individual  cases.  We  do  not  in- 
clude in  this  process  more  than  is  indicated  in  the 
premises,  and,  besides,  it  is  not  one  of  reasoning, 
which  Induction,  as  here  considered,  should  be. 

2d.  Imperfect  Induction.  —  Imperfect  Induc- 
tion is  the  process  by  -which  the  conclusion  extends  be- 
ypnd  the  data  upon  which  it  is  based,  as  Generaliza- 
tion does  not  go  beyond  it.  If  we  had  reasoned 
from  the  observed  fact  of  four  planets  revolving 
around  their  axes,  that  all  of  them  did  so,  we 
should  have  an  inductive  inference,  because  we 
infer  some  facts  not  observed.  This  is  the  true 
Inductive  reasoning.  Again,  if  I  observe  in  a 
number  of  cases  that  a  certain  kind  of  cloud  has 
been  accompanied  by  a  hail-storm,  and  infer  that 
this  will  always  follow  this  particular  kind  of 
cloud,  I  have  performed  an  Inductive  inference. 

3d.  Definition  of  Inductive  Reasoning. — There 
have  been  several  ways  of  defining  this  process. 
It  has  been  usual  to  contrast  it  with  Deduction. 
Now,  deduction  is  often  said  to  be  reasoning  from 
general  to  particular  truths,  from  the  containing 
to  the  contained  truth,  or  from  cause  to  effect. 
Induction,  therefore,  by  contrast  is  defined  as  rea- 
soning from  the  particular  to  the  general,  from 
the  contained  to  the  containing,  or  from  effect 
to  cause.  Sometimes  induction  is  said  to  be  rea- 
soning from  the  known  to  the  unknown.  This 
would  be  making  deduction,  by  contrast,  reasoning 
from  the  unknown  to  the  known,  which  is  absurd. 
The  former  ways  of  representing  it  are  much  the 
better. 

But  there  is  still  a  better  way  of   comparing 


INDUCTIVE    REASONING  187 

them.  Deduction,  we  saw,  is  reasoning  in  which 
the  conclusion  is  contained  in  the  premises.  This 
is  the  ground  of  its  certitude,  and  we  commit  a 
fallacy  whenever  we  go  beyond  the  premises,  as 
shown  by  the  laws  of  the  distribution  of  terms. 
In  contrast  with  this,  then,  we  may  call  inductive 
reasoning  the  process  by  which  we  go  beyond  the 
premises  in  the  conclusion.  This  is  illustrated 
in  such  examples  as  have  already  been  given  for 
imperfect  induction.  To  repeat  examples,  how- 
ever, if  we  observe  that  red  sunsets  are  frequently 
followed  by  clear  days,  we  may  infer  that  the 
same  coincidence  will  occur  in  the  future  ;  or  if 
we  observe  that  the  dew  falls  upon  clear  nights, 
and  that  clear  nights  are  accompanied  by  a 
peculiar  radiation  of  heat,  we  may  infer  a  causal 
connection  between  this  radiation  of  heat  and  the 
falling  of  the  dew.  Good  illustrations  also  of  this 
inference  are  Copernicus's  discovery  of  the  earth's 
motion  around  the  sun,  Kepler's  law  of  planetary 
motion,  Newton's  theory  of  gravitation,  the  undu- 
lative  theory  of  light  from  the  eclipse  of  the  satel- 
lites of  Jupiter,  etc. 

The  process  here  is  to  start  from  certain  given 
facts  and  to  infer  some  other  probable  fact  more 
general  or  connected  with  them.  In  this  we  see 
the  process  of  going  beyond  the  premises.  There 
are,  of  course,  certain  conditions  which  regulate 
the  legitimacy  of  this  procedure,  just  as  there  are 
conditions  determining  deduction.  They  are  that 
the  conclusion  shall  represent  the  same  general 
kind  as  the  premises,  with  a  possibility  of  acci- 
dental differences.  But  it  goes  beyond  the  prem- 


1 88  LOGIC   AND    ARGUMENT 

ises  in  so  far  as  known  facts  are  concerned.  This 
can  be  shown  best  by  studying  the  formal  process. 
II.  FORMAL  PROCESS  IN  INDUCTION.  — 
We  found  that  we  could  give  formal  expression 
to  deductive  reasoning  in  the  Moods  and  Figures 
of  the  syllogism.  The  same  can  be  done,  to  a 
limited  extent  at  least,  in  induction.  It  is  usual 
to  state  the  forms  for  induction  in  the  Second  and 
Third  Figures.  It  may  be  possible  to  do  it  in  all 
the  Figures,  but  we  do  not  require  in  this  work  to 
develop  the  formal  process  in  all  its  possibilities. 
Hence,  we  shall  take  those  forms  which  most 
clearly  exhibit  both  the  probability  of  the  infer- 
ence and  its  passage  beyond  the  premises.  We 
take  one  in  the  Second  Figure  : 

A        Magnets  attract  iron. 
A        Loadstones  attract  iron. 
A  .-.  Loadstones  are  magnets. 

•  In  deductive  reasoning  this  would  be  a  formal 
fallacy  of  undistributed  middle,  but  if  we  simply 
mean  to  suppose  from  the  common  attribute  of 
attraction  for  iron  that  the  two  classes  of  substance 
are  the  same,  and  hold  the  idea  as  a  probability 
merely,  we  are  entitled  to  regard  it  as  inductively 
legitimate.  This  is  to  say  that  the  agreement  of 
the  two  subjects  in  this  particular  suggests  that 
they  are  of  the  same  kind  in  general.  The  same 
kind  of  reasoning  can  be  illustrated  in  the  Third 
Figure  : 

A,  B,  C  attract  iron. 

A,  B,  C  are  magnets. 
/.  All  Magnets  attract  iron. 


INDUCTIVE    REASONING  189 

Here  we  have,  deductively,  a  fallacy  of  illicit 
minor,  but  inductively  an  inference  that  what 
proves  true  in  certain  known  cases  or  particulars 
will  prove  true  of  the  whole  class.  The  inference 
or  hypothesis  here  has  only  a  degree  of  proba- 
bility, and  is  not  a  necessary  one  as  in  deduction. 
The  term  hypothesis  or  supposition  expresses  ex- 
actly what  this  inductive  inference  is,  and  indi- 
cates how  it  is  that  we  go  beyond  the  premises 
or  actually  known  facts,  to  what  has  some  degree 
of  possibility  or  probability.  Thus,  to  illustrate 
again,  if  we  find  that  two  or  three  gases  are  com- 
pressible into  liquids  under  certain  degrees  of 
temperature  and  pressure,  we  may  well  suppose  it 
possible  or  probable,  and  to  that  extent  rational, 
that  other  gases  are  compressible  under  some 
similar  conditions.  The  supposition  may  require 
verification  or  proof  before  the  mind  is  satisfied, 
but  we  make  an  hypothesis  which  is  the  inference 
to  what  is  possible  or  probable,  this  varying  in 
degree  according  to  the  nature  and  number  of  the 
facts  upon  which  it  is  based. 

It  will  be  necessary  to  illustrate  inductive  rea- 
soning by  concrete  examples  which  do  not  repre- 
sent the  formal  process  to  which  they  can  be  re- 
duced. For  instance,  it  was  observed  that  there 
were  disturbances  in  the  movements  of  certain 
planets  which  could  not  be  accounted  for  by 
known  causes.  From  what  was  known  about 
causes  and  their  effects  in  general  it  was  inferred 
that  there  was  some  undiscovered  planet  which 
would  account  for  the  disturbance.  This  unknown 
planet,  not  being  included  in  the  premises  of  the 


I  go  LOGIC   AND    ARGUMENT 

reasoning,  is  thus  the  object  of  an  inductive  in- 
ference. It  is  a  conjectured  cause  of  a  known 
effect,  and  only  awaited  verification,  as  it  received 
this  by  the  experiments  of  Leverrier  and  Adams> 
in  order  to  become  an  assured  object  of  knowl- 
edge. Again,  it  was  observed  that  the  specific 
gravity  of  nitrogen  taken  from  the  air  is  greater 
than  nitrogen  taken  from  all  other  sources.  It 
was  inferred  from  this  that  there  must  be  some 
other  substance  to  account  for  this  difference. 
Finally,  argon  was  discovered.  Still,  again,  I  ob- 
serve the  rise  in  price  of  certain  stocks.  I  may 
infer  several  causes  of  it,  but  if  I  know  the  circum- 
stances well  enough,  I  may  infer  the  probability, 
for  instance,  that  some  agreement  is  maturing  be- 
tween rival  companies.  I  may  notice  again  that 
frequently  the  appearance  of  a  rainbow  is  followed 
by  clear  weather,  and  hence  may  infer  from  ob- 
servation in  any  particular  case  the  re-occurrence 
of  the  same  clear  weather.  In  all  of  these  in- 
stances my  reasoning  is  from  some  specific  facts 
to  a  general  rule  comprehending  more  than  the 
special  cases. 

III.  INDUCTIVE  FALLACIES — It  is  not  easy 
to  indicate  the  inductive  fallacies,  if  it  be  even 
possible,  in  the  formal  process  of  induction.  In 
deduction  they  consist  of  violating  the  laws  of  the 
quantification  of  terms  ;  that  is,  in  going  beyond 
the  premises  and  endeavoring  at  the  same  time 
to  retain  the  same  certitude  in  the  conclusion  as 
was  supposed  in  the  premises.  But  induction  per- 
mits us  to  transcend  the  premises,  quantitatively  at 
least,  and  there  can  hardly  be  any  formal  fallacies 


INDUCTIVE   REASONING  19 1 

in  this,  unless  we  except  the  case  of  negative 
premises.  But  all  this  is  a  matter  for  more  ad- 
vanced logic  to  determine.  It  is  certain,  how- 
ever, that  in  respect  to  the  subject-matter  of  the 
conclusion  in  inductive  reasoning  there  are  some 
very  definite  limitations  upon  the  right  to  tran- 
scend the  premises.  We  cannot  infer  anything  we 
please  from  any  premises  we  please.  We  must 
conform  to  certain  definite  rules  or  principles. 
Any  violation  of  them  will  be  a  fallacy.  These 
rules  are  the  same  as  those  for  material  fallacies 
in  deduction,  so  that  the  fallacies  of  induction, 
whether  they  are  ever  formal  or  not,  are  at  least 
material  ;  that  is,  they  occur  whenever  equivoca- 
tion and  presumption  are  committed.  There  are, 
then,  two  simple  rules  which  should  not  be  vio- 
lated, (i)  The  subject-matter  in  the  conclusion 
should  be  of  the  same  general  kind  as  in  the  prem- 
ises. (2)  The  facts  constituting  the  premises 
must  be  accepted  and  must  not  be  fictitious. 


CHAPTER    XIV 
PROOF    AND    ARGUMENTATION 

I.  INTRODUCTION Description,  Explana- 
tion, and  Exposition  were  examined  as  processes 
by  which  we  endeavor  to  narrate  facts  and  thoughts 
in  a  systematic  and  orderly  manner.  They  are 
designed  to  give  an  intelligible  and  methodical 
conception  of  the  data  that  are  connected  with  a 
particular  theme.  But  they  are  not  designed  to 
convince  the  mind.  They  may  incidentally  do 
this,  but  it  is  not  their  primary  object  to  create 
conviction.  They  are  occupied  with  the  forma- 
tion and  presentation  of  clear  conceptions,  syste- 
matic and  methodical  discourse,  which  does  as 
much  to  make  ideas  intelligible  as  it  does  to  please 
the  sense  of  order.  But  Proof  and  Argumenta- 
tion go  beyond  this.  They  endeavor  to  convince, 
to  remove  doubt,  to  give  belief  and  knowledge  to 
the  intellect.  It  will  be  necessary  to  examine  its 
nature  and  its  kinds. 

i st.  Nature  of  Proof. — Proof  is  defined  as  a 
method  of  producing  conviction  ;  that  is,  of  creat- 
ing assent  to  propositions.  This  assent  takes  two 
forms  :  Belief \  or  probable  truth  ;  and  Knowledge, 
or  certain  truth.  Whenever  any  proposition  is  as- 
serted or  made  the  subject  of  argument,  the  ob- 
192 


PROOF    AND    ARGUMENTATION 


193 


ject  is  to  show  whether  it  be  true  or  false.  The 
general  method  of  argumentation  is  the  same  for 
both  sides.  But  the  proposition  at  the  outset  is 
supposed  not  to  represent  any  conviction  in  favor 
of  or  against  itself,  but  to  be  balanced  between 
belief  and  disbelief,  or  certitude  and  denial.  The 
problem  is  to  influence  the  judgment  so  that  it 
will  decide  in  favor  of  or  against  the  proposition. 
Proof  or  Confirmation  is  the  process  of  determin- 
ing the  conviction  one  way  or  the  other,  and  of 
removing  the  balance  or  doubt  so  that  some  de- 
gree of  assent  or  denial,  whether  of  belief  or 
knowledge,  will  follow  as  a  consequence.  The 
process  is  effected  in  various  ways  as  the  kinds 
of  proof  will  show. 

One  important  point  in  the  nature  of  proof 
must  not  be  neglected.  It  is  somewhat  different 
from  inference,  though  it  is  reasoning.  Inference 
properly  proceeds  from  premises  to  conclusion  ; 
proof  proceeds  from  conclusion  to  premises. 
Proof  assumes  that  a  proposition  is  first  asserted 
or  stated  and  then  established.  In  inference  the 
premises  are  given  and  the  conclusion  is  found, 
but  in  proof  the  conclusion  is  given  and  the 
premises  found  for  establishing  it.  This  is  clearly 
illustrated  by  the  process  of  debating  where  the 
issue  is  first  defined  and  then  proved.  We  state 
our  proposition  as  a  fact,  and  then,  assuming  that 
it  is  doubted  by  others,  proceed  to  find  the  prem- 
ises, or  propositions,  which  include  it  and  which 
enforce  conviction  upon  the  doubter.  Proof  is, 
therefore,  technically  speaking,  a  process  the  re- 
verse of  inference,  though  it  succeeds  in  establish- 
13 


LOGIC    AND    ARGUMENT 

ing  the  same  fact,  inference  being  the  process  for 
finding  it. 

2<3.  Kinds  of  Proof.  —  The  kinds  of  proof  or 
argumentation  assume  two  general  forms,  Direct 
and  Indirect,  and  each  of  these  may  be  subdivided 
into  two  forms.  Direct  proof  or  argumentation 
consists  in  the  attempt  to  establish  a  given  propo- 
sition ;  indirect  proof  consists  in  refuting  objec- 
tions to  it.  Each  of  these  may  be  divided  into 
deductive  and  inductive  argumentation,  and  as  the 
method  of  arranging  the  data  for  proof  or  dis- 
proof is  the  same  in  both  the  direct  and  the  in- 
direct forms  of  it,  there  will  be  little  necessity  for 
dwelling  at  any  length  on  these  general  divisions. 
It  will  suffice  to  illustrate  direct  and  indirect 
proof. 

A  case  of  direct  proof  is  found  deductively  in 
the  proposition  demonstrating  that  the  angles  of 
a  triangle  are  equal  to  two  right  angles,  or  infer- 
ring that  the  ancestors  of  land  crabs  were  once 
marine  crabs  from  the  existence  of  intermediate 
and  amphibious  species.  Here  consistent  and 
pertinent  matter  is  mentioned  in  which  the  con- 
clusion is  contained,  or  which  suggests  it  as  prob- 
able. A  case  of  indirect  proof  of  the  same  propo- 
sitions would  be  the  reductio  ad  absurdum  of  the 
contradictory  proposition  of  the  first  instance, 
and  a  removal  of  apparent  contradictions  in  the 
second  instance.  Thus,  if  to  disprove  the  marine 
ancestry  of  land  crabs  it  be  asserted  that  the  one 
is  physiologically  constructed  to  live  in  water  and 
the  other  is  not,  we  should  effectively  remove  the 
force  of  this  objection  to  the  original  assertion 


PROOF    AND    ARGUMENTATION 


'95 


by  showing  that  to-day  there  are  species  of  ani- 
mals which  are  born  and  live  for  a  period  in  the 
water,  and  afterward  live  on  land.  This  is  a  case 
of  indirect  proof  by  removing  objections. 

The  general  method  of  deductive  proof  is  ex- 
plained in  the  discussion  of  deductive  reasoning. 
All  that  remains  to  be  remarked  here  is  that  it  is 
to  be  resorted  to  whenever  we  wish  to  give  certi- 
tude to  the  proposition  asserted.  In  choosing  our 
premises  and  facts,  therefore,  we  must  be  careful 
to  select  those  which  really  include  the  conclu- 
sions. Any  other  procedure  will  involve  one  of  the 
formal  or  material  fallacies.  Thus,  if  the  thesis 
to  be  proven  is  that  "  The  punishment  of  Socrates 
was  unjust,"  my  premises  must  be  stated  so  as  to 
include  this  as  an  instance.  I  can  assume  that  the 
punishment  of  innocent  men  is  unjust,  and  then 
prove  that  Socrates  was  an  innocent  and  right- 
eous man.  But  if  my  major  premise  be  "Most 
wise  men  should  be  exempt  from  punishment," 
the  proof  would  be  impossible.  The  proof,  there- 
fore, when  demonstration  is  to  be  attained,  must 
represent  the  conclusion  as  clearly  comprehended 
in  the  premises. 

In  inductive  proof  this  requirement  is  not  im- 
perative. The  conclusion  is  only  probable  and 
represents  a  preference  in  this  respect  over  the 
alternative  course.  Hence,  it  is  sufficient  to  show 
that  the  conclusion  is  enough  like  or  connected 
with  other  facts  to  be  probably  included  in  them 
in  regard  to  the  matter  at  issue.  Thus,  if  I  find  a 
man  dishonest  in  a  certain  number  of  transactions, 
I  may  expect  to  find  him  so  in  the  future  or  in 


196  LOGIC   AND    ARGUMENT 

other  transactions.  This  is  not  a  necessary  con- 
sequence, but  only  a  probable  one.  In  an  argu- 
ment, therefore,  we  must  be  careful  to  distinguish 
between  this  kind  of  proof  and  the  deductive 
process.  We  must  see  that  we  are  not  confusing 
the  inductive  with  the  deductive  proof.  Other- 
wise we  are  liable  to  a  charge  of  fallacy.  If  we 
recognize  that  our  proof  is  inductive,  the  argu- 
ment against  us  must  be  inductive,  unless  the  con- 
tradictory of  our  proposition  can  be  deductively 
proved,  in  which  case  inductive  evidence  of  our 
thesis  is  impossible. 

II.  PROCESS  OF  PROOF  OR  ARGUMENT. 
— There  is  always  a  definite  order  of  events  in 
the  proper  presentation  of  proof.  We  have  to 
remember  that  the  object  is  to  convince,  and  not 
merely  to  please.  But  to  effect  this  end  we  should 
not  plunge  into  a  debate  without  knowing  what 
both  the  nature  and  the  compass  of  the  issue  is. 
The  presentation  of  arguments  is  the  final  stage 
of  the  process  in  producing  conviction.  The  first 
thing  is  to  make  the  issue  clear.  Then  we  have 
to  show  how  much  ground  it  covers.  Finally,  we 
have  to  present  the  proofs.  These  three  proc- 
esses may  be  called  Definition,  Division  c-  Analysis, 
and  Probation.  Each  will  come  up  in  order  for 
treatment. 

i st.  Definition. — In  an  argument  definition  is  the 
process  of  determining  the  nature  of  the  issue  or 
thesis  to  be  proved  or  disproved.  The  thesis  will 
be  some  proposition  for  or  against  which  argu- 
ments are  to  be  produced.  But  before  the  argu- 
ments can  be  seen  to  have  pertinency  we  must 


PROOF    AND    ARGUMENTATION 


I97 


know  exactly  what  is  to  be  proved  or  disputed. 
Propositions  are  often  equivocal,  and  only  careful 
definition  can  make  clear  what  is  to  be  defended  or 
opposed.  Thus,  in  the  simple  proposition  "  Man 
is  mortal,"  there  may  be  a  doubt  about  the  issue. 
Whether  the  predicate  "  mortal  "  is  to  be  affirmed 
or  denied  of  the  subject  will  depend  as  much 
upon  what  we  mean  by  the  subject  "  man  "  as  upon 
the  nature  of  the  predicate.  The  issue  here  is  the 
connection  between  the  subject  and  predicate.  If 
we  define  "  man  "  as  the  particular  animal  organ- 
ism which  we  know  as  having  certain  qualities, 
our  proposition  will  mean  one  thing.  If  we  define 
the  term  as  the  abstract  subject  of  consciousness 
without  reference  to  the  animal  organism,  our 
proposition  will  mean  another.  Again,  if  "  man  " 
means  the  race  of  individual  organisms,  the  prop- 
osition will  mean  still  another  thing.  Our  argu- 
ments must  be  different  for  each  aspect  of  the 
question.  It  is  so  with  every  thesis.  Take  again 
the  proposition  "  Protection  is  beneficial  to  the 
country."  Here  the  first  duty  in  determining 
what  the  issue  under  debate  may  be,  is  to  define 
carefully  what  is  meant  by  "protection."  There 
is  the  etymological  import  of  the  term,  which 
would  be  rejected  here  as  not  indicating  specifi- 
cally enough  what  was  meant.  Then  there  is  the 
broad  conception  of  prevention  of  any  kind  of  in- 
jury to  citizens,  which  would  define  the  object  of 
all  civil  laws.  This  might  not  be  the  issue  in- 
tended. Then  there  is  lastly  the  economic  policy 
of  taxing  certain  imports  for  the  benefit  of  the 
producer.  This  conception  would  indicate  the 


198  LOGIC   AND    ARGUMENT 

issue  usually  understood  by  such  a  proposition 
This  illustrates  a  definition  of  the  subject.  But 
the  predicate  equally  demands  definition  in  many, 
if  not  all,  cases.  We  must  make  clear  what  we 
mean  by  "  beneficial  to  the  country."  We  must 
indicate  whether  the  issue  regards  economic  or 
moral  benefits,  or  both.  The  arguments  will  be 
very  much  affected  by  this  distinction.  But  in  all 
cases  we  must  make  the  issue  clear  by  definition 
in  order  to  prepare  the  mind  for  estimating  the 
pertinence  of  the  argument,  as  well  as  for  enabling 
the  debater  himself  to  select  pertinent  and  valid 
proofs.  The  rules  for  determining  the  definition 
have  been  given  already  in  their  proper  place. 

2d.  Analysis. — Analysis  or  division  is  the  proc- 
ess of  showing  how  many  specific  and  different 
aspects  of  an  issue  are  involved  in  it  and  which 
can  be  separated  for  distinct  treatment.  The 
process  recognizes  a  classification  and  logical  or- 
der for  the  several  arguments  to  be  produced.  It 
may  also  be  defined  as  the  process  of  supplying 
the  topics  for  the  discourse  or  argument.  Suppose 
we  have  the  thesis  "  Literature  civilizes  man." 
The  analysis  into  topics  may  extend  to  both  the 
subject  and  the  predicate.  We  simply  apply  the 
principles  of  division  to  each  term  in  order  to 
determine  the  several  topics  or  aspects  of  the 
issue. 

The  importance  of  this  process  after  definition 
is  that  it  enables  the  debater  to  discuss  a  part  of 
his  theme  at  a  time,  and  not  expose  the  whole  of 
it  to  attacks  that  may  be  based  upon  its  general 
and  abstract  meaning.  Thus,  if  we  divide  "  liter- 


PROOF    AND    ARGUMENTATION  199 

ature  "  into  its  various  form  to  speil  "  scientific 
philosophic,  historical,  etc.,  or  other  forms,  we  can 
select  one  division  at  a  time  for  probation,  in 
which  it  may  be  easier  to  establish  the  claim  as- 
serted than  in  some  other  case,  and  in  this  way 
we  can  produce  at  least  a  presumption  in  favor  of 
others.  Hence,  in  trying  to  show  that  "  Literature 
civilizes  man,"  we  can  divide  the  subject  first  into 
a  series  of  topics.  Thus,  we  could  have  the  prop- 
osition "  Polite  literature  civilizes  man,"  and  again 
subdivide  "  polite  literature "  into  prose  and 
poetry,  and  each  of  these  into  its  further  subdi- 
visions, so  as  to  bring  out  the  merits  and  influence 
of  each  in  the  process  of  civilization.  Then  we 
could  proceed  to  show  that  "  Scientific  literature 
civilizes  man,"  and  also  resort  to  various  subdi- 
visions here.  But  the  nature  of  the  influence  of 
scientific  thought  is  different  from  that  of  polite 
literature.  It  affects  the  interests  and  character 
of  men  in  a  different  way.  Hence,  it  is  convenient 
to  separate  the  treatment  of  the  one  aspect  of 
the  issue  from  the  other.  It  will  be  the  same 
with  the  other  two  divisions,  "  philosophic"  and 
"  historical  literature."  Similarly  a  series  of  top- 
ics may  be  deduced  from  an  analysis  of  the  predi- 
cate. We  may  divide  the  civilizing  process  into 
"  the  elevation  of  artistic  literary  taste,"  "  the  re- 
finement of  manners,"  "  the  extension  of  knowl- 
edge," "  the  improvement  of  morals,"  etc.  All  of 
these  maybe  regarded  as  processes  in  civilization, 
and  we  have  to  show  that  literature  either  in  its 
parts  or  as  a  whole  does  or  does  not  accomplish 
these  results.  In  this  way  we  give  a  variety  of  as- 


200  LOGIC   AND    ARGUMENT 

pects  to  the  issue,  and  prepare  the  mind  to  esti- 
mate it  more  clearly  while  the  discourse  may  be 
more  logical  and  effective. 

The  process  just  illustrated  is  that  of  division. 
But  a  thesis  or  subject  may  be  analyzed  into  topics 
by  partition.  This  process  has  already  been  ex- 
plained. It  names  the  properties  connected  by  a 
conception  or  theme.  Hence,  we  may  supply  the 
aspects  of  an  issue  in  argument  by  partition  either 
of  subject  and  predicate,  or  the  proposition  as  a 
whole,  as  well  as  by  division.  Thus,  if  we  have  the 
thesis  "  Monarchy  is  the  best  form  of  government," 
we  may  analyze  the  issue  by  partition  so  as  to 
show  what  has  to  be  sustained  or  disproven  in  the 
following  manner.  For  the  thesis  we  might  fix  on 
the  several  characteristics  that  define  monarchy 
as  a  government  :  (i)  The  simplicity  of  mon- 
archy ;  (2)  The  efficiency  of  monarchy  ;  (3)  The 
venerable  nature  of  its  power  ;  (4)  The  influence 
of  monarchy  upon  science  and  art,  etc.,  to  almost 
any  extent  we  might  please.  Against  the  thesis 
we  might  produce  counter  characteristics :  (i) 
The  irresponsibility  of  its  power  ;  (2)  The  ten. 
dency  to  nepotism  ;  (3)  Its  historical  habit  of  in- 
terfering with  human  liberty  ;  (4)  Its  inadjusta- 
bility  to  social  and  economic  progress,  etc. 

All  themes  or  issues  can  be  analyzed  in  this 
way,  and  the  value  of  the  process  is  simply  that 
which  has  already  been  indicated  ;  namely,  the  dis- 
tinction and  logical  classification  of  arguments  so 
as  to  aid  the  mind  in  the  formation  of  its  convic- 
tions and  the  systematization  of  its  ideas.  The 
next  process  is  Probation. 


PROOF    AND    ARGUMENTATION  2OI 

3d.  Probation.  —  Probation  is  the  process  of 
proof,  the  statement  and  arrangement  of  facts  and 
truths  which  will  establish  belief  or  knowledge  in 
regard  to  the  proposition  at  issue,  or  the  contrary. 
The  thesis  or  issue  is  the  proposition  to  be  proved 
or  disproved.  The  truths  which  prove  or  dis- 
prove it  are  the  known  facts  and  principles  which 
may  constitute  the  premises,  and  the  thesis  will 
be  the  conclusion.  These  determining  truths  may 
be  axioms,  postulates,  proved  propositions,  or  any 
truth  or  fact  which  the  person  to  whom  the  pro- 
bation is  presented  may  accept.  Their  accept- 
ance is  the  condition  of  their  proving  or  disprov- 
ing anything.  We  must  observe,  therefore,  that 
probation,  as  here  discussed,  is  a  material  as  well 
as  a  formal  process.  The  object  in  proof  is,  not 
merely  to  have  correct  reasoning,  but  also  to  have 
correct  and  true  propositions.  We  must,  there- 
fore, enunciate  some  facts  or  principles  accepted 
by  the  person  to  whom  the  probation  is  presented, 
and  then  bring  the  thesis  or  issue  under  it  in  such 
a  way  as  to  enforce  conviction,  or  at  least  make  it 
the  most  probable  alternative.  As  thus  defined, 
however,  there  are  two  general  types  of  this  pro- 
bation which  we  may  consider.  They  are  the 
Deductive  and  the  Inductive  arguments. 

i.  Deductive  Arguments. — These  are  arguments 
that  endeavor  to  give  perfect  certitude  to  the 
proposition  affirmed  or  denied.  I  give  an  illus- 
tration of  its  method  from  mathematics.  Suppose 
I  am  asked  to  prove  that  the  sum  of  the  angles  of 
a  triangle  is  equal  to  two  right  angles.  If  now  I 
can  show  either  by  observation  or  proof  that  the 


202 


LOGIC    AND    ARGUMENT 


sum  of  the  angles  of  a  triangle  is  equal  to  some 
quantity  which  is  known  or  admitted  immediately 
to  be  equal  to  two  right  angles,  I  can  then  draw 
the  conclusion  desired.  The  demand  and  the 
attempt  to  give  proof  assumes  that  the  proposi- 
tion cannot  be  immediately  seen  to  be  true,  at  least 
in  the  special  concrete  case.  Hence,  I  try  to  find 
some  known  truth  in  which  the  concrete  case  is 
evidently  included.  I  first  construct  my  triangle 
as  follows  : 


cL 


The  thing  to  be  proved  is  the  assertion  that 
a  +  b  4-  c  =  two  right  angles.  Now  we  know  by 
construction  that  c  +  d  +  e  =  two  right  angles. 
The  triangle  is  also  by  construction  a  right-angled 
triangle,  so  that  c  is  a  right  angle  and  also  d  +  e 
make  a  right  angle.  By  drawing  the  line,  separat- 
ing d  and  e,  parallel  with  the  hypothenuse  of  the 
triangle,  we  make  b  =  d  and  a  =  e,  according  to  a 
proposition  in  geometry  here  assumed.  The  ar- 
gument then  takes  the  following  form  : 

c  +  d  +  e  —  two  right  angles. 
a+b  +  c  =  c  +  d  +  e. 
.•.a  +  b  +  c  =  two  right  angles. 

He  who  admits  the  two  premises  must  thus 
admit  the  proposition  which  was  to  be  proved.  It 
is  the  same  with  any  other  proposition,  such  as 


PROOF   AND    ARGUMENTATION  203 

"  Democracy  is  the  proper  form  of  government." 
If  it  is  to  be  proved,  its  identity  or  inclusion  in 
some  other  admitted  proposition  must  be  seen  ; 
that  is,  we  must  see  that  it  follows  from  some 
other  known  fact. 

There  are  no  special  subdivisions  of  this  form  of 
argument  except  the  categorical,  the  hypothetical, 
and  the  disjunctive  syllogism.  These  have  already 
been  explained,  and  it  remains  only  to  mention 
certain  advantages  which  one  or  two  of  them  may 
have  over  others.  The  disjunctive  syllogism  has 
the  value  of  confining  the  issue  when  the  debater 
is  careful  to  observe  the  demand  for  complete  dis- 
junction. The  hypothetical  argument  has  the  ad- 
vantage of  getting  the  conclusion  admitted  on  the 
condition  that  the  minor  premise  is  proved.  It 
designs,  therefore,  to  limit  the  duty  of  proof  to 
the  minor  premise  by  getting  consideration  for 
the  major  premise  without  committing  the  affirm- 
ative to  a  categorical  assertion  of  it.  It  is  the 
connection  between  it  and  the  conclusion  that  is 
to  be  gained  with  a  reservation  for  the  minor 
premise  which  has  probably  to  be  proved,  and 
which,  as  representing  a  simple  matter  of  fact, 
may  be  easy  of  proof.  Hence,  there  are  situations 
in  which  these  forms  of  argument  are  preferable 
to  the  categorical ;  but  the  debater  must  use  his 
own  insight  as  to  the  proper  emergencies  for  the 
application  of  them.  Disproof,  of  course,  employs 
the  same  method,  and  only  tries  to  establish  a  con- 
trary or  contradictory  proposition. 

2.  Inductive  Arguments. — There  are  arguments 
that  endeavor  to  show  why  the  conclusion  is 


204  LOGIC    AND    ARGUMENT 

preferable  to  any  other  supposition.  They  should 
always  be  recognized  as  such  by  the  person  pre- 
senting them,  if  he  wishes  to  escape  the  charge  of 
certain  formal  and  material  fallacies.  The  in- 
ductive argument  consists  in  the  statement  of  the 
facts  which  suggest  the  rationality  of  the  conclu- 
sion. Suppose  the  thesis  is  to  maintain  that  the 
earth  moves  around  the  sun.  When  Copernicus 
advanced  this  doctrine  he  had  only  an  inductive 
argument  to  favor  it.  This  consisted  in  a  few 
simple  facts  which  his  theory  would  explain,  but 
which  did  not  appear  to  necessitate  it.  They 
were  first  the  facts  that  night  and  day  and  the 
seasons  were  as  consistent  with  his  conception  as 
with  the  Ptolemaic,  while  the  apparent  retrograde 
motions  of  the  heavenly  bodies  were  more  simply 
explained  by  his  than  by  the  opposing  doctrine. 
In  the  course  of  time  the  case  was  taken  as  proved, 
but  at  first  all  that  could  be  asserted  was  that 
some  facts  suggested  it  and  made  it  possible  or 
probable.  Or  again,  A  is  bitten  by  a  cobra,  and 
the  inference  is  that  he  will  die.  Now,  if  I  can 
assume  as  certain  that  all  who  are  bitten  by  the 
cobra  must  die,  the  reasoning  would  be  deductive. 
But  it  may  be  that  all  my  knowledge  in  the  case 
is  limited  to  the  fact  that  some  who  have  been 
bitten  by  the  cobra  die.  Instead,  therefore,  of 
having  deductive  proof,  I  have  only  the  inductive. 
It  will  stand  as  follows  : 

Some  (X.  Y.  Z.)  bitten  by  the  cobra  die. 
A  is  bitten  by  the  cobra. 
.'.  A  will  die. 


PROOF   AND    ARGUMENTATION  2O$ 

Here  the  conclusion  can  only  be  probable  in  so 
far  as  the  premises  are  concerned,  and  the  man 
who  relies  upon  this  method  of  proof  escapes  the 
necessity  of  proving  the  universality  of  the  major 
premise,  and  requires  only  to  show  a  sufficient 
number  of  actual  facts  either  easily  provable  or 
readily  admitted  in  order  to  give  at  least  some 
possibility  to  the  thesis  to  be  established,  pro- 
vided, of  course,  that  he  observes  the  material 
conditions  for  inference  of  any  kind.  Many  prop- 
ositions, perhaps,  are  capable  only  of  inductive 
proof,  and  the  proper  sagacity  must  be  shown  in 
deciding  this  matter. 

III.  CLASSIFICATION  AND  ARRANGE- 
MENT OF  ARGUMENTS The  deductive  and 

inductive  arguments  which  have  been  discussed 
assume  various  forms  according  to  the  purpose 
which  they  are  made  to  serve.  But  they  are  not 
classified  according  to  the  form  of  the  reasoning. 
They  are  considered  from  the  kind  of  force  or 
cogency  which  they  represent  in  producing  con- 
viction. As  to  the  arrangement  of  them,  there 
must  be  some  conception  of  the  special  situation 
before  any  rules  can  be  laid  down  absolutely 
about  it.  The  general  principle  is  that  the  order 
of  arguments  must  depend  upon  the  state  of  the 
mind  or  minds  addressed  and  the  order  of  de- 
pendence in  the  proofs.  Hence,  we  may  lay  down 
two  general  rules  which  determine  the  order  of 
stating  arguments,  and  which  will  be  considered 
after  classifying  the  kinds  of  arguments. 

ist.  Forms  of  Argument.  —  Here  we  have  to 
do,  not  with  merely  formal  processes,  but  with 


206  LOGIC    AND    ARGUMENT 

certain  material  aspects  and  relations  of  facts  and 
truths  which  give  rise  to  interest  and  conviction. 
They  may  be  classified  as  follows  : 

1.  Analytic  Arguments. — These  are  merely  the 
analysis  and  presentation  of  what  the  very  con- 
ception of  the  thesis*  and  its  terms  involves.     It 
partakes  usually  of  the  nature,  or  at  least  the  cer- 
titude, of  deduction,  and  also  of  definition.  Rather 
it  represents  an  analysis  of  all  that  is  implied  in 
the  contents  of  definition.     For  instance,  suppose 
the  issue  is  "  Protection   is  inexpedient."     After 
defining   protection    as  a  tax"  on  goods  not  pro- 
duced by  a  country  in  order  to  encourage  such 
production,   it  may  be  seen   that  such  a  tax  in- 
volves   in    its   very    conception    a  discrimination 
against  unprotected  consumers,  and  therefore  in- 
expedient or  even  unjust.     This  conclusion  is  the 
result  of  mere  analysis,  or  inference  from  the  con- 
ceptions in  the  thesis  as  premises. 

2.  Synthetic  Arguments. — Analytic  arguments  are 
of  the  nature  of  deductions  or  inferences  from  the 
ideas  contained  in  or  implied  by  the  thesis  itself. 
But  synthetic  arguments  are  of  the  nature  of  re- 
gressive proof,  going  back  to  premises  containing 
the  thesis  as  a  conclusion.     It  is  thus  a  process  of 
finding  a  truth   containing  the  proposition   to  be 
proved,  and  enough  more  usually  to  make  it  true, 
whatever   we    may    think    of   the    proposition    at 
stake.     Thus,  in  the  thesis   "  Protection  is  inex- 
pedient," we  should   seek  the  assertion   of  some 
general  and  unquestionable  truth,  such  as  "  Any 
policy  which  favors  one  class  at   the  expense  of 
another  is  inexpedient."     This  is  a  major  premise 


PROOF   AND    ARGUMENTATION  207 

which  will  gain  easy  admission,  or  impose  a  heavy 
task  upon  an  opponent  to  refute  it,  and  hence  it 
leaves  the  affirmative  the  easier  task  of  proving 
that  the  minor  premise  is  contained  in  it  as  the 
necessary  link  in  the  chain  leading  to  the  conclu- 
sion. The  synthetic  feature  in  it  is  the  fact  that 
the  thesis  seems  to  be  or  is  a  necessary  conse- 
quence of  two  or  more  independent,  or  apparently 
independent,  truths.  It  is  deductive  in  its  nature, 
as  it  has  been  illustrated  ;  but  it  is  not  deductive 
in  the  sense  that  it  starts  from  definition  and  mere- 
ly shows  that  the  proposition  is  a  consequence  of 
that  definition,  but  it  is  deductive  only  in  the 
sense  that  it  necessarily  follows  from  two  prem- 
ises mediated  by  the  third  term  and  is  included 
in  them.  But  the  synthetic  argument  involves  the 
difficulty  of  making  good  the  assertion  of  truths 
that  contain  something  more  comprehensive  than 
the  particular  conclusion  at  issue.  It  is  possible 
also  to  give  the  synthetic  argument  an  inductive 
character.  It  becomes  so  according  to  the  nature 
of  the  premises. 

3.  Argument  from  Antecedent  Possibility. — This 
argument  is  sometimes  called  antecedent  proba- 
bility, but  antecedent  possibility  is  better.  It 
means  the  argument  which  shows  that  there  is 
nothing  opposed  to  the  supposition  under  discus- 
sion. It  may  be  considered  a  form  of  indirect 
argument.  It  proves  that  it  is  not  against  reason 
to  suppose  the  apriori  possibility  of  the  proposi- 
tion, and  leaves  to  other  positive  evidence  the 
proof  of  the  proposition  as  a  fact.  Suppose  the 
issue  is  whether  there  is  any  immaterial  substance 


208  LOGIC   AND   ARGUMENT 

or  not.  It  is  an  antecedent  possibility  to  show 
that  the  conception  of  such  a  rea'ity  does  not 
contradict  any  known  reality.  It  is  not  the  slight- 
est evidence  of  the  fact.  No  such  immaterial 
reality  may  exist  as  a  fact.  But  it  is  no  reason  to 
deny  it  that  there  is  no  positive  evidence  for  it. 
Hence,  wherever  there  is  a  tendency  to  deny  the 
existence  of  something  on  the  ground  of  the  want 
of  evidence,  it  is  a  defence  of  its  possibility  to  show 
that  no  facts  stand  in  the  way  of  supposing  it,  so 
that  positive  belief  or  conviction  only  awaits  evi- 
dence. In  regard  to  the  particular  instance  be- 
fore us,  this  argument  for  antecedent  possibility 
consists  in  showing  that  the  known  facts,  or  the 
limits  of  positive  knowledge  only  extend  to  the 
denial  of  evidence  for  immaterial  substance,  and 
not  to  the  denial  of  its  existence.  The  error,  of 
course,  in  assuming  the  latter  on  the  ground  of 
the  former,  has  its  counter  error  in  the  assumption 
of  its  existence  because  it  cannot  be  positively  de- 
nied. But  we  must  be  as  careful  to  avoid  this  use 
of  the  argument  as  we  are  desirous  of  impeaching 
the  opposite  side  for  committing  the  counter 
error.  We  must  be  careful  to  show  that  the  ar- 
gument is  only  indirect,  and  not  direct. 

One  form  of  this  argument  for  antecedent  pos- 
sibility is  the  so-called  argument  from  Analogy, 
which  is  based  upon  the  resemblance  of  relations 
rather  than  upon  the  resemblance  of  properties  be- 
tween things.  For  instance,  the  argument  from 
the  habitation  of  the  earth  to  the  habitation  of 
other  planets  is  one  of  analogy  ;  or  again,  from 
the  metamorphosis  of  the  butterfly  to  immortality. 


PROOF    AND    ARGUMENTATION  209 

These  arguments  are  often  taken  for  real  ones, 
but  in  so  far  as  they  are  arguments  at  all  they  are 
only  indirect  and  of  a  weak  kind  even  at  that.  In 
fact,  it  might  be  possible  to  maintain  that  the 
chief,  if  not  the  only,  function  of  analogy  is  to  de- 
fine a  conception  or  issue.  But  there  are  probably 
uses  of  it  where  it  avails  to  establish  an  antece- 
dent possibility,  though  it  can  do  no  more  than 
this. 

4.  Argument  from    Circumstantial    Evidence. 

This  is  a  form  of  inductive  and  synthetic  proof, 
and  is  that  form  of  argument  which  endeavors 
to  prove  a  thesis  by  the  presence  of  certain  signs 
or  incidents  which  suggest  it.  For  instance,  I 
have  to  show  that  light  has  velocity.  If  I  can 
point  to  the  phenomenon  or  fact  that  there  is  a 
difference  of  time  in  the  observation  of  the 
eclipses  of  certain  satellites,  determined  by  the 
position  of  the  earth  in  its  orbit,  I  may  safel'y 
maintain  that  my  thesis  has  some  probability. 
If  I  can  collect  a  number  of  concurrent  facts,  I 
strengthen  that  probability.  A  still  better  in- 
stance is  the  following  :  A  man  is  charged  with 
murder.  We  wish  to  prove  the  accusation.  We 
find  certain  characteristics  in  the  boot-tracks  go- 
ing away  from  the  murdered  person.  If  we  find 
that  the  boots  of  the  accused  correspond  exactly 
to  these  characteristics,  we  have  at  least  presump- 
tive evidence  of  his  guilt.  If,  further,  we  find  that 
the  accused  possesses  bullets  or  slugs  like  those 
found  in  the  body  of  the  murdered  person,  we 
have  corroborative  circumstantial  evidence.  Un- 
less this  can  be  of  a  large  and  cumulative  amount 
14 


210  LOGIC    AND    ARGUMENT 

or  of  a  particular  quality,  it  does  not  suffice  for 
demonstrative  proof,  but  only  establishes  a  certain 
degree  of  probability.  It  is  simply  an  argument 
from  certain  signs,  marks,  characteristics,  coinci- 
dences, etc.,  to  the  probability  that  a  given  thesis 
is  true.  Whenever  we  argue  from  any  given  at- 
tribute or  phenomenon  to  an  unknown  cause,  we 
in  fact  employ  the  argument  from  circumstantial 
evidence,  though  the  phrase  is  usually  limited  to 
legal  situations  and  problems,  where  the  data 
from  which  the  inference  is  drawn  are  not  usually, 
if  ever,  attributes  of  anything,  but  events  and 
facts  apparently  independent  of  the  thing  to  be 
proved. 

5.  Personal  Argument. — This  argument  may  be 
regarded  as  a  form  of  circumstantial  evidence, 
though  it  is  not  what  we  should  call  the  ad  rem 
argument,  but  what  I  should  technically  call  the 
argumentum  ad personam.  So  far  as  the  real  issue 
is  concerned,  this  class  of  arguments  is  comprised 
in  that  which  I  have  called  the  evasio  dictionis,  and 
includes  the  argumentum  ad  judicium,  argumentum 
ad  populum,  argumentum  ad  hominem,  etc.  These, 
we  have  shown,  may  be  legitimate  if  they  are  di- 
rected to  produce  conviction,  but  not  tor  proving  the 
truth.  In  debate  or  argumentative  discourse  the 
first  object  is  to  produce  conviction  ;  that  is,  agree- 
ment or  disagreement  in  regard  to  the  issue,  and 
the  material  truth  must  then  depend  upon  other 
processes  than  mere  reasoning.  In  order  that  one 
side  or  the  other  may  thus  establish  this  result,  it 
is  necessary  that  each  shall  be  allowed  to  present 
a  form  of  argument  that  involves  the  other  in  the 


PROOF   AND   ARGUMENTATION  211 

conclusion  which  the  latter  denies.  This  is  a  way 
of  indicating  that  the  truth  lies  on  the  side  of 
consistency,  only  it  does  not  finally  decide  upon 
which  side  the  consistency  lies.  If,  for  instance, 
the  issue  is  "  The  appointing  power  of  the  execu- 
tive should  be  increased,"  and  the  affirmative 
quotes  A  as  an  authority  in  his  favor,  it  is  perfect- 
ly pertinent  for  the  negative  to  quote  in  reply  the 
same  authority  for  facts  which  contradict  this  con- 
clusion. This  is  an  ad  hominem  argument  against 
the  affirmative,  and  requires  either  the  abandon- 
ment of  his  authority  or  the  acceptance  of  the 
negative's  conclusion.  In  the  appeal  to  universal 
consent,  or  to  the  convictions  of  the  audience, 
there  is  the  effort  to  present  facts  with  some  pre- 
sumptive weight  in  the  conclusion  to  be  sustained. 
It  is  the  same  with  the  argumentum  ad  verecundiam. 
But  the  authority  to  which  appeal  is  made  in  this 
case  must  be  recognized  by  the  opponent. 

6.  Argument  from  Testimony. — This  is  a  form  of 
argument  based  upon  the  credibility  of  a  witness 
to  real  or  alleged  facts.  The  facts  are  circum- 
stantial evidence  of  the  thesis,  and  the  character 
of  the  witness  is  the  measure  of  the  weight  at- 
taching to  his  testimony  on  the  facts.  "  The  de- 
gree of  weight  to  be  attributed  to  testimony  is 
always  to  be  estimated  by  this  view  of  the  nature 
of  testimony — that  it  is  a  sign,  implying  the  facts 
to  which  it  testifies  as  more  or  less  necessary 
conditions  of  its  having  been  given.  Whenever, 
therefore,  occasions  or  motives  exist  in  the  case 
for  giving  the  testimony  other  than  the  truth,  the 
credibility  of  the  witness  will  be  so  far  impaired. 


212  LOGIC   AND    ARGUMENT 

We  are  thus  to  judge  of  the  credibility  of  histor- 
ians. The  historian  of  a  sect  or  of  a  party  must 
be  received  as  a  credible  witness  only  so  far  as  it 
may  appear  that  truth  was  the  condition  of  his 
speaking  as  he  does.  All  admissions  against  his 
own  sect  or  party,  unless  made  as  baits  or  lures, 
wil-1  be  received  as  honest  testimony.  If  these 
qualifications  are  wanting,  there  is  nothing  on 
which  testimony  can  rest."  But  where  honesty 
and  candor,  as  well  as  good  judgment,  exist,  the 
facts  attested  will  have  all  the  weight  of  these 
qualities,  though  this  may  not  be  so  great  as  in 
the  case  that  the  facts  are  personally  known  by 
the  disputants. 

This  argument  from  testimony  takes  two  forms  : 
(i)  Testimony  in  regard  to  facts,  and  (2)  Testi- 
mony representing  matters  of  opinion.  The  latter 
involves  the  results  of  judgment  and  inference,  and 
the  former  does  not  go  beyond  matters  of  per- 
ception, in  which  more  people  are  competent  to 
pronounce  than  in  matters  involving  interpreta- 
tion and  inference.  The  second  form  is  some- 
times called  "expert  evidence."  It  me:;: 
accept  the  judgment  of  qualified  men  where  com- 
mon experience  is  not  a  guide. 

2d.  Arrangement  of  Arguments. — The  general 
principles  which  regulate  the  order  of  stating  the 
arguments  are  two.  They  are  :  (i)  The  state  of 
the  mind  addressed  ;  (2)  The  dependence  of  the 
arguments  upon  each  other. 

"  If  the  mind  addressed  be  already  in  a  state  of 
belief,  and  the  object  of  the  discourse  is  to  con- 
firm and  strengthen  it,  then  the  weaker  arguments 


PROOF    AND    ARGUMENTATION  213 

may  generally  need  to  be  placed  first,  and  the 
stronger  ones  last.  But  if  there  be  an  opposing 
belief  to  be  set  aside,  it  will  be  better  to  advance 
the  stronger  first,  in  order  to  overthrow  opposi- 
tion at  once.  The  weaker  may  follow,  which  will 
confirm  when  they  would  be  of  no  avail  in  the 
first  assault.  In  order  to  leave  a  strong  impres- 
sion, however,  some  of  the  stronger  arguments 
may  be  reserved  for  the  close  ;  or  what  is  equiva- 
lent, the  arguments  may  be  recapitulated  in  the 
reverse  order." 

When  it  comes  to  the  consideration  of  the  sec- 
ond principle,  which  disregards  the  state  of  mind 
addressed,  we  have  an  order  that  may  not  repre- 
sent the  order  of  strength  in  producing  convic- 
tion, but  an  order  in  which  the  strength  itself  may 
be  affected  by  what  goes  before.  The  succeeding 
arguments  are  supposed  to  receive  additional 
weight  from  the  cogency  of  the  preceding.  Other 
things  being  equal,  therefore  we  have  the  follow- 
ing rules  : 

(1)  Deductive  should  precede  inductive  proofs. 
This  assumes  that  they  are  both  applicable  to  the 
issue.     In  case  that  only  one  of  them  is  possible, 
this  rule  does  not  apply,  and  in  case  that  the  state 
of  mind  is  already  one  of  belief,  the  order  should  be 
reversed.     Those  also  who  maintain  that  induc- 
tion conditions  deduction  might  adopt  the  reverse 
of  this  order. 

(2)  Analytic  proofs   should    precede    the    syn- 
thetic and  all  others.     The  reason  for  this  rule  is 
that  the  analytic  argument  naturally  follows  the 
process  of  definition,  and  prepares  the  way  for 


214  LOGIC    AND    ARGUMENT 

the  reference  to  general  principles  or  particular 
facts  antecedent  to  the  proposition  stating  the 
issue,  while  the  analytic  argument  does  not  go  be- 
hind the  conceptions  which  define  this  issue. 

(3)  Antecedent  possibility  arguments  should 
precede  the  inductive  arguments  generally  and 
those  from  circumstantial  evidence  in  particular. 
If  any  presumption  against  the  possibility  of  the 
thesis  exists,  the  first  thing  is  to  get  that  out  of 
the  way,  and  the  mind  is  then  receptive  for  the 
others. 

But  there  are  no  hard-and-fast  rules  to  be  fol- 
lowed for  every  thesis.  The  judgment  of  the 
debater  must  be  used  first  to  gauge  the  situation 
and  to  adopt  the  best  arrangement  to  suit  it  with 
a  general  reference  to  the  rules  just  mentioned. 
The  debater  must  decide  in  each  particular  case 
both  the  state  of  mind  addressed  and  the  pro- 
priety of  using  the  cumulative  method  of  argu- 
ment. In  all  cases,  however,  no  matter  what  the 
technical  name  given  to  the  kind  of  argument,  the 
cumulative  argument  has  great  value  and  weight. 
This  is  the  successive  presentation  of  arguments 
that  grow  in  cogency  and  power,  and  the  order 
will  depend  somewhat  upon  circumstances.  The 
order  here  will  be  first  antecedent  possibility, 
testimony,  circumstantial  evidence,  personal  argu- 
ment, and  deduction.  This  procedure  must  or 
ought  to  be  concluded  by  a  recapitulation  which 
sums  up  in  outline  all  the  arguments  that  have 
been  presented.  Just  as  definition  introduces  dis- 
course, recapitulation  should  close  it. 


QUESTIONS   AND   EXAMPLES 

CHAPTER   I 

INTRODUCTION 

1.  Define  Logic,  and  show  when  it  is  a  science  and 
when  an  art. 

2.  Define  Rhetoric,  and  show  its  relation  to  Logic. 

3.  Explain  the  various  meanings  of  the  term  "  law," 
and  more  especially  its  usage  in  Logic. 

4.  What  is  the  meaning  of  the  term  "  thought  ?  " 

5.  Name  the  prelogical  processes. 

6.  Define  the  logical  processes,  and  state  the  common 
characteristic  of  all  of  them.     What  is  the  distinction 
between  perceiving  and  apperceiving  ? 

7.  What  is  the  name  of  the  two  kinds  of  Conceptions, 
and  what  do  they  mean  ? 

8.  Define  Judgment  and  Reasoning,  and  distinguish 
between  them. 

9.  What  are  the  divisions  of  Idea-expression  ? 

10.  Define  a  "  theme,"  and  the  processes  of  Explana- 
tion and  Confirmation. 

11.  What  is  meant  by  "  analysis  "  and  "synthesis" 
in  Discourse  ? 

CHAPTER   II 

1.  What  is  a  Term  or  Concept  ? 

2.  What    are   Categorematic   and   Syncategorematic 

Terms  ? 

215 


2l6  LOGIC    AND    ARGUMENT 

3.  Define  and  distinguish  between  Singular  and  Gen- 
eral Terms. 

4.  Define  and  distinguish  between  Collective  and  Dis- 
tributive Terms  ;  also  between  Concrete  and  Abstract 
Terms. 

5.  What  is  the  popular  meaning  of  Abstract  and  Con- 
crete Terms,  and  how  is  it  distinguished  from  the  logical 
and  technical  meaning  ? 

6.  In  the  following  list  of  Terms  select  the  various 
kinds  of  them,  and  explain  why  they  are  such,  stating 
whether  they  are  pure  or  mixed  : 


Act, 

Beauty, 

Man, 

Ability, 

Presidency, 

Action, 

Timeliness, 

Virtue, 

Excellence, 

Wisdom, 

Agency, 

Plato, 

Solitude, 

Dexterity, 

Government, 

Agent, 

Library, 

Introduction, 

Art, 

Production, 

Warmth, 

Science, 

Truth, 

Stone, 

Paper, 

Society, 

Personality, 

Wood, 

Army, 

House, 

Sun, 

Washington, 

Chair, 

Nation, 

Sweetness, 

Some, 

Bible, 

History, 

Koran, 

Prime  Minister. 

7.  Explain  the  uses  of  Terms  in  the  following  propo- 
sitions and  passages  : 

(a)  The   inhabitants   of  Germany   constitute   a 

nation. 

(b)  "  All  men  find  their  own  in  all  men's  good, 

And  all  men  join  in  noble  brotherhood  " 

(f)  All  standing  armies  are  dangerous  to   the 

state. 

(d)  Non  omnis  moriar  (i.e.,  I  shall  not  all  die). 

(e)  All  the  men  cannot  lift  this  weight. 
(/)  Virtue  brings  its  own  reward. 

(g)  Society  is  an  organism. 

(h)  All  of  the  regiment  was  put  to  flight. 

(z)  Duty  cannot  be  evaded  when  the  nation  is- 
sues a  call  to  arms  for  the  defence  of  its 
dignity  and  humanity.  Justice  and  right 
must  be  secured,  even  if  the  people  cannot 
form  a  united  resistance  to  an  enemy.  All 


QUESTIONS    AND    EXAMPLES  217 

the  moral  forces  and  interests  of  the  com- 
munity ought  to  be  arrayed  with  the  gov- 
ernment in  such  an  emergency,  and  when 
the  country's  chief  ruler  issues  his  com- 
mand for  action  and  obedience. 
8.  Select  and  explain  the  various  uses  of  the  following 

Terms,  Positive,  Negative,    Privitive,  and   Nego-posi- 

tive  : 


Tree, 

Animal, 

Deaf, 

Inhuman, 

Inconclusive, 

Insensible, 

Ignorant, 

Peerlesi, 

Perfect, 

('nartistic, 

Useful. 

Impure, 

Defect, 

Decarnate, 

Inconvenient, 

Blind. 

Clean, 

Cold, 

Dislike, 

Imperishable, 

Pure, 

Bitter, 

Naked, 

Inordinate, 

Uncontrollable. 

9.  Define  and  explain  Infinitated,  Absolute,  and  Rel- 
ative Terms. 


CHAPTER   III 

1.  What  is  meant  by  the  Predicables? 

2.  What  is  meant  by  the  Quantity  and  Quality,  or  Ex- 
tension and  Intension  of  Terms  ? 

3.  Define  Genus  and  Species.      What  is  the  relation 
between  them  ? 

4.  Explain  the  meaning  of  Conferentia   and   Differ- 
entia, and  show  their  relation  to  each  other. 

5.  Explain  the  meaning  of  Essentia  and  Accidentia. 

6.  What  is  the  relation  between  Extension  and  In- 
tension ? 

7.  What  is  the  analysis  of  Concepts  ?    Name  its  forms. 

8.  Explain  and  illustrate  the  processes  of  Definition, 
Division,  and  Partition.     What  are  the  rules  for  each  ? 

9    Give  a  logical  definition  for  each  of  the  following 
concepts : 

Biped,  Nation,  Diet,  Spirit,  Water,  Honor, 

House,  Mind,  Republic,  Action,  Religion,  Imagination, 

Club,  Money,  Matter,  Spectacle,  Science,  Government, 

Flood.  Politics,  Poetry,  Picture,  Heat,  Gravitation. 


2l8  LOGIC   AND    ARGUMENT 

10.  Examine  the  following  definitions  : 

(a)  A  chair  is  a  thing  on  which  men  sit. 

(b)  Ink  is  a  black  liquid. 

(c)  Philosophy  is  knowledge. 

(d)  An  animal  is  a  thing  which  increases  in  size. 

(e)  A  nation  is  a  collective  body  of  men. 

(f)  A  triangle  is  a  figure  which  is  formed  by  the 

intersection  of  three  straight  lines. 

(g)  Death  is  the  opposite  of  life. 

(h)  A  king  is  one  who  exercises  regal  functions. 
(/)  A  gentleman  is  a  man  who  has  no  visible 

means  of  subsistence. 
(_/)  Man  is  a  rational  animal  of  the  highest  form 

of  development. 
(k)  Science  is  the  study  of  phenomena  with  a 

view  to  scientific  knowledge. 
(/)  Religion  is  a  theory  of  divine  government. 
(/«)  Faith  is  the  substance  of  things  hoped  for, 

the  evidence  of  things  not  seen. 
(«)  Legislatures  are  bodies  of  law-makers. 
(o)  Members  of  the  solar  system  are  anything 

over  which  the  sun  exercises  an  influence. 
(/))  Socialism  is  a  theory  of  government. 

11.  Apply  Logical  Division  to  the  following  Concepts  : 

Tree,  Religion,  Matter,  Quadrupeds,  Vertebrates, 

Stones,  House,  Machines,  Organisms,  Literature, 

Science,  Books,  Vegetables,  Churches,  Employment, 

Poetry,  Laws,  Substance,  Mammals,  Societies. 

12.  Divide   "man"   according    to    color,   language, 
and  religion  ;   "  government"  according  to  constitution, 
territory,  and  race  ;  "  houses  "  according  to  form,  ar- 
chitecture, use,  and  history  ;  "vegetables  "  according  to 
structural  form,  use,  habitat,  and  history  ;  "  language  " 
according  to  form,  geographical  distribution  ;  "  matter'1 
according  to  density,  structure,  and  use;  "books"  ac- 
cording to  form,  subject,  binding,  price,  age,  and  utility. 


QUESTIONS    AND    EXAMPLES  219 

13.  Divide  each  of  the   following  concepts  according 
to  two  distinct  principles  of  division  : 

Law,          Occupations,        Metals,        Religion,  History, 

Society,      Triangle,  Liquids,      Instruments,     Animals. 

14.  Analyze  the  following  concepts  by  partition  : 

Metal,  Picture,  Cathedral,  Knowledge,  Religion,  Ink, 

Iron,  Stone,  Honor,  Money,  Literature,  Book, 

Plant,  House,  Water,  Virtue,  Production,  Ice, 

German,  Diamond,  Vertebrate,  Sensation,  Gravitation,  Wheat. 

15.  Apply  Partition  to  the  following  abstract  concep- 
tions so  as  to  exhibit  their  qualities  either  of  action  or 
passion  : 

Politeness,     Beauty,         Comity,         Manliness,     Courtesy, 
Wisdom,        Justice,         Credulity,     Purity,  Confidence, 

Generosity,    Penitence,    Patriotism,    Genius,          Spirituality. 


CHAPTER   IV 

1.  Define  Analysis  of  a  theme  in  Discourse.     What 
processes  constitute  it  ? 

2.  What  is  the  place  of  Definition   in   Explanatory 
Discourse  ? 

3.  What  are  the  uses  of  Division  and  Partition  in  the 
same  ? 

4.  How  is  Analysis  to  be  applied  ? 

5.  Define  Synthesis  in  Discourse. 

6.  What  are  the  laws  that  regulate  Synthesis  or  Com- 
position? 

7.  Define  each  of  the  three  forms  of  Composition. 

8.  Describe  the  following  subjects  or  themes  accord- 
ing to  the  various  classes  of  attributes  suggested  by  Par- 
tition : 

The  Zodiac  ;  America  ;  Boston  ;  Mont  Blanc  ;  Web- 
ster's  Dictionary  ;   a  tree  ;  a  locomotive  ;   an  electric 


220  LOGIC    AND    ARGUMENT 

telegraph  ;  a  book  ;  a  diamond  ;  the  yErieid  ;  Paradise 
Lost;  Dante's  Inferno  ;  England;  The  character  of  Na- 
poleon ;  Bismarck  ;  Ohio  ;  United  States ;  Atlantic 
Ocean  ;  a  statesman  ;  a  philosopher  ;  a  poet ;  a  laborer  ; 
Raphael's  Madonna  ;  a  legislature. 

The  elephant  ;  quadrupeds  ;  a  manufactory  ;  store  ; 
true  manhood  ;  genius  ;  politeness  ;  a  horse-race  ; 
plants  ;  electricity  ;  commerce  ;  inflation  of  the  cur- 
rency ;  candor  ;  temporal  power  of  the  Pope  ;  civiliza- 
tion of  the  present  century ;  a  winter  landscape  ;  the 
medieval  Church ;  the  government  of  England ;  the 
Roman  religion  ;  Christianity ;  commerce  ;  Greek  art  ; 
political  institutions. 

9.  Apply    Narration    to    the    following  themes   with 
analysis  : 

The  Crusades  ;  the  American  Revolution  ;  the  Amer- 
ican Constitution  ;  the  progress  of  Art ;  the  battle  of 
Gettysburg  ;  the  French  Revolution  ;  the  Life  of  Glad- 
stone, of  Bismarck,  of  Pitt ;  the  glacial  epoch  ;  the 
formation  of  habit ;  the  growth  of  a  plant ;  a  boat-race  ; 
a  game  of  ball ;  a  railway  collision  ;  the  rise  of  chival- 
ry ;  the  slave  trade  ;  the  history  of  Protection,  of  Free- 
trade  ;  the  growth  of  intelligence  ;  currency  problems 
in  the  United  States  ;  growth  of  the  Speaker's  power  in 
Congress  ;  American  architecture,  etc. 

10.  Apply  Exposition  to  the  following  themes  with 
analysis  : 

Government ;  religion  ;  science  ;  property  ;  politics  ; 
virtue  ;  dress  ;  rhetoric  ;  manners  ;  society  ;  art  ;  music  ; 
painting  ;  sculpture  ;  personality  ;  the  Church  ;  archi- 
tecture ;  the  Papacy  ;  protestantism  ;  the  social  con- 
tract ;  the  Constitution  ;  the  Declaration  of  Indepen- 
dence ;  justice;  commerce;  business;  law;  literature; 
currency  ;  magnanimity  ;  self-reliance  ;  poverty  ;  civil- 
ization ;  democracy ;  empire. 


QUESTIONS   AND    EXAMPLES  221 


CHAPTER  V 

1 .  Define  a  Proposition  and  distinguish  between  Univ- 
ocal  and  Equivocal  Propositions.     Illustrate. 

2.  Define  and  illustrate  each  of  the  Logico-Grammati- 
cal  Propositions. 

3.  What  are  the  symbols  of  each  of  these  propositions, 
and  how  distinguish  them  in  respect  to  form  and  matter  ? 

4.  Define  and  illustrate  both  the  Logico-Qualitative 
and  the  Logico-Quantitative  Propositions. 

5.  How  do  we  reduce  the  five-fold  division  of  proposi- 
tions into  the  two-fold  ? 

6.  State,  define,  and  illustrate  the  divisions  of  Equivo- 
cal Propositions. 

7.  What  are  the  symbols  for  each  of  the  Equivocal 
Propositions,  and  how  reduce    them   to  the   Univocal 
form  ? 

8.  What  is  meant  by  the  Distribution  of  terms  ?  What 
is  the  distribution  of  terms  in  Definitions  and  Exclusive 
Propositions  ? 

9.  Examine  the   following   propositions  and   resolve 
them  into  their  proper  forms  for  definite  logical  use  : 

(a)  Man  is  rational. 

(b)  All  men  are  not  wise. 

(c)  Only  bipeds  have  hands. 

(d)  Man  alone  is  not  obedient  to  his  instincts. 

(e)  Few  elements  are  metals. 
(/)  Most  men  are  Caucasians. 

(g)  Only  those  substances  which  are  not  subject 

to  gravity  are  immaterial. 
(h)  All  persons  except  criminals  and  foreigners 

are  not  allowed  to  vote. 


222  LOGIC   AND   ARGUMENT 


CHAPTER  VI 

1.  What  is  meant  by  the  Opposition  of  Propositions  ? 

2.  How  do  we  treat  singular  and  abstract  proposi- 
tions ? 

3.  If  we  assume  the  falsity  of  any  one  of  the  four 
propositions,  A,  E,  I,  and  O,  what  follows  in  regard  to 
the  others  ? 

4.  How  may  we  disprove  propositions,  and  which  is 
the  better  form  of  disproof  ? 

5.  What  are  the  laws  of  Opposition  ? 

6.  Select  pairs  of  the  following  propositions  and  ar- 
range them  so  as  to  show  all  the  various  relations  illus- 
trated by  them  : 

(a)  All  metals  are  elements. 

(b)  Some  metals  are  not  elements. 

(c)  No  metals  are  elements. 

(d)  Some  metals  are  elements. 

(e)  Most  metals  are  elements. 

(f)  All  metals  are  not  elements. 

(g)  Not  all  metals  are  elements. 
(h)  Only  metals  are  elements. 
(0  Few  metals  are  elements. 

7.  Examine  the  relation  expressed  by  the  following 
propositions  : 

(a)  One  man  says  that  all  men  are  wise  and  an- 

other that  they  are  all  ignorant. 

(b)  Free  trade  lowers  prices  and  protection  does 

not. 

(c)  One  party  asserts  that  A  will  be  elected  presi- 

dent, and  the  other  that  B  will  be  elected 
president. 

(d)  Mr.  X  asserts  that  not  a  nail  was  made  in 

this  country  before  1861.  E  says  that  so 
far  from  this  statement  of  X  being  true  that 
in  1856  there  were  2,645  nail-machines  in 


QUESTIONS    AND    EXAMPLES  223 

operation  in  this  country  with  an  output  of 
86,462  tons,  and  in  1859  as  many  as  4,686,- 
207  pounds  of  nails  were  exported. 

(e)  Will  the  educated  woman  marry  ?  So  queried 
one  of  our  alumnae  in  a  recent  magazine 
article  in  which  the  object  was  to  show  that 
she  would  not.  The  review  roll  of  our 
alumnae  shows  that  of  76  ladies  who  grad- 
uated in  our  classes,  32  have  already  mar- 
ried. 

(/)  The  policy  which  he  now  says  would  have 
been  infamous  he  was  then  proposing  to 
adopt. 

(g)  If  the  appreciation  of  gold  has  been  the 
cause  of  the  extraordinary  fall  in  prices, 
why  have  ivory  and  whalebone  not  fallen 
in  price,  but  on  the  contrary  have  steadily 
risen  in  price  during  the  last  decade  ? 


CHAPTER   VII 

1.  What  is  the  meaning  of  inference?     Of  immediate 
inference  ?     Of  mediate  inference  ? 

2.  Name  the  divisions  of  immediate  inference. 

3.  What  are   the   rules   for  conversion  ?      What   is 
meant  by  Convertend  and  Converse  ? 

4.  What  propositions  can  be  converted  and  what  not, 
and  why  ? 

5.  Why  cannot  proposition  I  be  contraverted  ? 

6.  Why  are  Definitions  and   Exclusive  propositions 
real  or  apparent  exceptions  to  these  rules  ? 

7.  What  is  the  technical  meaning  of  the  exclusive 
particle  ? 

8.  What  is  meant  by  Conversion  by  Negation  ? 

9.  What  are  the  rules  for  Obversion  and  Contraver- 
sion  ? 


224  LOGIC    AND    ARGUMENT 

10.  How  do  we  obvert  negative  propositions  ? 

11.  Define  and  illustrate  inference  by  Contribution. 

12.  What  is  the  difference  between  the  two  kinds  of 
Contribution  ? 

13.  Define  and  explain  Antithesis. 

14.  State  the  logical  process  by  which  we   pass  from 
each  of  the   following  propositions   to  the   succeeding 
one  : 

(a)  All  oaks  are  trees. 

(b)  No  oaks  are  not  trees. 

(c)  No  not-trees  are  oaks. 

(d)  All  not-trees  are  not-oaks. 

(e)  All  not-trees  are  not  oaks. 
(/)  All  oaks  are  not  not-trees. 
(g)  All  oaks  are  trees. 

(h)  All  not-trees  are  not  oaks. 
(/)  All  not-trees  are  not-oaks. 
(j)  Some  not-oaks  are  not-trees. 
(k)  Some  not-oaks  are  not  trees. 
(/)  Some  oaks  are  trees,     (a) 
(m)  Some  trees  are  oaks. 
(«)  No  trees  are  oaks. 
(o)  All  trees  are  oaks. 

15.  Apply  the  various  processes  of  immediate  infer- 
ence to  the  following  propositions  : 

(a)  Every  man  is  a  biped. 

(b)  Some  books  are  dictionaries. 

(c)  The  virtuous  alone  are  happy. 

(d)  No  triangle  has  one  side  equal  to  the  sum 

of  the  other  two. 

(e)  "  Every  consciousness  of  relation  is  not  cog- 

nition." 

(/)  Perfect  happiness  is  impossible. 
(g)  A  stitch  in  time  saves  nine. 
(//)  None  think  the  great  unhappy  but  the  great. 
(*')  Few  are  wise  enough  to.be  virtuous. 
(j)  No  one  is  free  who  does  not  control  himself. 


QUESTIONS    AND    EXAMPLES  225 

(k)  Good  orators  are  not  always  good  statesmen. 

(/)  Some  inorganic  substances  do  not  contain 
carbon. 

(m)  Only  the  brave  deserve  the  fair. 

(«)  All  men  are  not  born  equal. 

(<?)  No  one  is  a  hero  to  his  valet. 

(P)  Uneasy  lies  the  head  that  wears  a  crown. 

(g)  He  jests  at  scars  who  never  felt  a  wound. 

(r)  Better  late  than  never. 

(s)  Every  mistake  is  not  culpable. 

(t)  I  shall  not  all  die.     (Non  omnis  mortar.) 

(u)  Fain  would  I  climb  but  that  I  fear  to  fall. 

(v)  Great  is  Diana  of  the  Ephesians. 

(TV)  Not  many  of  the  metals  are  brittle. 

(x)  Talents  are  often  misused. 

(y)  Some  books  are  to  be  read  only  in  part. 

(z)  Two  blacks  will  not  make  a  white. 

(a)  Not  one  of  the  Greeks  at  Thermopylae  es- 
caped. 

(b1)  Nothing  is  praiseworthy  but  virtue. 

(c)  No  one  is  always  happy. 

(d1)  There  is  none  good  but  one. 

(e)  All  that  glitters  is  not  gold. 

(f)  He  can't  be  wrong  whose  life  is  in  the  right. 
(g')  Philosophers  in  many  instances  do  not  es- 
cape equivocation. 

16.  State  the  relation,  if  any,  between  the  following 
propositions  as  indicated  by  the  figures  in  parentheses  at 
the  end  of  each  proposition  : 

(i.)  Good  men  are  wise. 

(2.)  Unwise  men  are  not  good  (i). 

(3.)  Some  wise  men  are  good  (i). 

(4.)   No  good  men  are  unwise  (i),  (2). 

(5.)  Some  unwise  men  are  not  good  (2),  (3),  (4). 

(6.)  Some  good  men  are  wise  (i),  (2),  (3). 

(7.)  No  good  men  are  wise  (i),  (3),  (4),  (6). 

(8.)  Some  good  men  are  not  wise  (i),  (3),  (6),  (7). 
15 


226 

(9.)  No  unwise  men  are  good  (i),  (4),  (5),  (8). 
(10.)  No  wise  men  are  good  (i),  (2),  (6),  (7),  (8). 

17.  What  is  the  logical  relation,  if  any,  between   the 
two    following  propositions  :    "A  false  balance  is  an 
abomination  to  the  Lord,  but  a  just  weight  is  his  de- 
light." 

18.  State  the  relation    between  the  following  three 
propositions  :  "  The  voluntary  muscles  are  all  striped, 
and  the  unstriped  are  all  involuntary,  but  a  few  of  the 
involuntary  muscles  are  striped." 

19.  Can  we  logically  infer  that  cold  contracts  bodies 
because  heat  expands  them  ? 


CHAPTER   VIII 

1.  Define  mediate  reasoning  with  its  divisions. 

2.  Name  and  define  the  elements  of  the  syllogism. 

3.  What  are  the  chief  rules  for  the  syllogism  ? 

4.  Define  what  is  meant  by  the  Mood  and  the  Figure 
of  the  syllogism. 

5.  Show  by  the  rules  what  Moods  must  be  rejected 
from  the  whole  sixty-four  on  the  ground  of  being  fal- 
lacious in  all  cases. 

6.  What  kind  of  conclusion  can   be  drawn  from  the 
following  premises,  AA,  EA,  IA,  AE,  OA,  El  ? 

7.  What  is  meant  by  a  weakened  conclusion  ? 

8.  Show   in    what    Figures    the    following    premises 
give  valid    conclusion :    AA,    AE,    IA,    EA,   AO,   El, 
AI,  OA. 

9.  Why  must  the  major  premise  of  the  first  Figure 
be  universal  ? 

10.  Why  must  one  of  the  premises  in  the  second  Fig- 
ure be  negative  ? 

1 1.  Show  that  O  cannot  stand  as  either  premise  in  the 
first  Figure,  as  major  premise  in  the  second  Figure,  and 
as  minor  premise  in  the  third  Figure. 


QUESTIONS    AND    EXAMPLES 


227 


12.  What  fallacy  will  be  committed  by  having  A  as  a 
conclusion  in  any  figure  but  the  first? 

13.  What  fallacy  is  committed  when  the  minor  pre- 
mise is  negative  in  the  first  and  third  Figures  ? 

14.  If  one  premise  be  O,  what  must  the  other  be  ? 

15.  Why  cannot  the  premises  be  IE  ? 

16.  Why  can  no  universal  conclusion  be  drawn  in  the 
third  Figure  ? 

r    17.  Could  you  reason  with  affirmative  propositions  in 
the  second  Figure  if  one  of  the  premises  is  a  definition  ? 

1 8.  How  can  you  treat  premises  in  IE  in  order  to  get 
a  valid  conclusion  ? 

19.  If  my  conclusion  be  O,  what  are  my  premises  ? 

20.  If  the  minor  premise  be  affirmative,  what  moods 
will  give  a  valid  conclusion  ? 

21.  State  the  Moods  and  Figures  of  the  following  syl- 
logisms, and  name  those    which    are  valid  and  those 
which  are  invalid  : 

(a)  Some  M  is  P.  (6)  All  P  is  M.  (c)  All  S  is  M. 

No  S  is  M.                                 No  M  is  S.  No  P  is  M. 

.'.  Some  P  is  not  S.  .'.  No  P  is  S.  .'.  Some  S  is  not  P. 

(rf)  No  M  is  P.  (e)  Some  P  is  M.  (/)  All  P  is  M. 

All  M  is  S.                                 All  S  is  P.  Some  M  is  not  S. 

.'.  Some  S  is  not  P.  .'.  Some  S  is  M.  .'.  Some  P  is  not  S. 

(g]  Some  M  is  not  S. 
Some  P  is  not  S. 

22 .  With  E  as  a  middle  term,  form  a  syllogism  with 
C  as  the  predicate  of  the  conclusion. 

23.  How  can  you  reduce  one  Figure  of  the  syllogism 
to  another  ? 

24.  What  is  the  value  of  each  Figure  of  the  syllogism  ? 

25.  Examine  the  following  syllogisms  : 

(a)  All  feathered  animals  are  vertebrates. 
No  reptiles  are  feathered  animals. 

/.  Some  reptiles  are  not  vertebrates. 

(b)  All  vices  are  reprehensible. 
Emulation  is  not  reprehensible. 

/.  Emulation  is  not  a  vice. 


228  LOGIC    AND    ARGUMENT 

(c)  All  men  are  rational  beings. 

All  Caucasians  are  rational  beings. 
.'.  All  Caucasians  are  men. 

(d)  All  vices  are  reprehensible. 
Emulation  is  not  a  vice. 

.  \  Emulation  is  not  reprehensible. 

(e)  Some  men  are  wise. 

All  philosophers  are  men. 

. '.  Some  philosophers  are  wise. 

(/)  Some  animals  are  quadrupeds. 

All  trees  are  not  quadrupeds. 
.'.  Some  trees  are  not  animals. 
(g)  Only  citizens  are  voters. 

ABC  are  voters. 
.'.ABC  are  citizens. 
(h)  Some  statesmen  are  wise. 

Some  good  men  are  statesmen. 
.'.  Some  good  men  are  wise. 
(/)    Some  plants  are  deciduous. 

No  trees  are  plants. 
.'.  Some  trees  are  not  deciduous. 
26.  Deduce  conclusions,  stating  Moods  and  Figures, 
from  the  following  premises  : 

(a)  All  planets  are  heavenly  bodies. 

No  planets  are  self-luminous. 
(6>)  All  Europeans  are  Caucasians. 
All  Caucasians  are  white. 

(c)  All  lions  are  carnivora. 

All  carnivora  are  devoid  of  claws. 

(d)  Some  animals  are  quadrupeds. 
All  quadrupeds  are  vertebrates. 

(e)  Oak  trees  are  evergreen. 
Pine  trees  are  evergreen. 

{/)  Some  Americans  are  not  white. 
All  white  persons  are  Caucasian. 


QUESTIONS   AND    EXAMPLES 


CHAPTER   IX 


229 


1.  Define  each  form  of  simple  and  complex  syllogism 
or  reasoning. 

2.  How  can  the  enthymeme  be  completed  to  form  a 
syllogism  ? 

3.  What  are  the  conditions  of  a  valid  sorites  ? 

(a)  Europeans  are  Caucasians  because  they  are 

white. 

(b)  We  cannot  know  what  is  false  because  knowl- 

edge cannot  be  deceptive. 

(c)  I  am  at  liberty  to  do  as  I  please,  since  he  did 

not  deliver  the  message. 

(d)  A  is  B  because  it  is  C. 

(e)  A  is  B  because  C  is  B. 

E  is  A  because  C  is  A. 
Eis  A. 

(/)  A  manor  cannot  begin  at  this  day,  because  a 
court  baron  cannot  now  be  founded. 


CHAPTER   X 

1.  What  is  the  difference  between   categorical   and 
hypothetical  reasoning  ? 

2.  Define  each  kind  of  hypothetical  reasoning. 

3.  Give  the  rules  for  valid  hypothetical  reasoning. 

4.  To  what  in  the  categorical  syllogism  are  the  moods 
of  hypothetical  reasoning  equivalent  ? 

5.  What  characterizes  simple  and  complex  dilemmatic 
reasoning  ? 

6.  How  can   hypothetical   reasoning   be   reduced   to 
categorical  ? 

7.  Examine  the  following  instances  of  hypothetical 
reasoning,  state  the  moods  and  convert  into  categorical 
syllogisms  : 


230  LOGIC    AND    ARGUMENT 

(a)  If  education  is  necessary  it  will  be  popular. 
It  is  popular,  and  therefore  will  be  neces- 
sary. 

(&)  Rain  has  fallen  if  the  ground  is  wet  ;  but  the 
ground  is  not  wet ;  and  therefore  rain  has 
not  fallen. 

(c)  If  the  citizens  would  reform  themselves  their 

government  might  be  improved  ;  but  the 
citizens  will  not  change  their  character, 
and  hence  no  improvement  in  their  gov- 
ernment can  be  expected. 

(d)  If  rain  has  fallen  the  ground  is  wet ;  but  rain 

has  not  fallen,  and  therefore  the  ground  is 
not  wet. 

(e)  If  the  weather  is  cloudy  it  will  not  be  warm  : 

but  it  is  warm,  and  therefore  is  not  cloudy. 

(f)  If  food  is  not  scarce  the  wants  of  the  com- 

munity are  satisfied  ;  but  food  is  not  scarce 
and  hence  the  wants  of  the  community 
are  satisfied. 

(g)  The  ground  is  wet  if  rain  has  fallen  ;  the 

ground  is  wet ;  therefore  rain  has  fallen. 

(k]  If  citizens  do  not  obey  the  law,  they  will  not 
retain  their  freedom ;  but  they  obey  the 
law  and  hence  retain  their  freedom. 

(*)  If  the  ground  is  wet  rain  has  fallen.  But 
rain  has  fallen  ;  therefore  the  ground  is 
wet. 

(/)  If  a  man  cannot  make  progress  toward  per- 
fection, he  must  be  a  brute  ;  but  no  man 
is  a  brute,  and  therefore  is  capable  of  such 
progress. 

(k)  If  two  and  two  make  five  in  some  other 
planet,  Mill's  opinion  about  the  matter  is 
correct ;  but  they  do  not  make  five  in  any 
place,  and  hence  Mill  is  wrong. 


QUESTIONS    AND    EXAMPLES 


CHAPTER   XI 


231 


1.  Define  and  illustrate  disjunctive  reasoning. 

2.  Explain  the  uses  of  the  symbols  of  disjunctive  prop- 
ositions. 

3.  Name   and   define   the   two  moods  of  disjunctive 
reasoning. 

4.  Upon  what  does  incomplete  disjunction  depend  ? 

5.  What  fallacy  characterizes  disjunctive  reasoning  ? 

6.  Examine  the  following  instances  of  disjunctive  rea- 
soning, and  resolve  into  both  hypothetical  and  categori- 
cal syllogisms: 

(a)  Criminals  are  either  good  or  bad. 
They  are  bad. 

They  are  not  good. 

(b)  The  weather  will  be  either  clear  or  warm. 
It  will  not  be  warm. 

It  will  be  clear. 

(c)  A  is  either  B  or  C. 
A  is  not  B. 

A  is  C. 

(d)  Aristotle  was  either  very  talented  or  very  in- 

dustrious. 

He  was  very  industrious. 
He  was  not  very  talented. 

CHAPTER   XII 

1.  Give   the   definition   and   divisions  of  the  several 
kinds  of  fallacy. 

2.  What  determines  the  existence  of  formal  fallacies  ? 

3.  How  do  we  classify  the  material  fallacies  ? 

4.  Define  and  distinguish  between  the  two  kinds  of 
fallacy  based  upon  equivocation. 

5.  Define  and  illustrate  the  fallacies  tf  petitio  principii 
and  non  sequitur. 


232  LOGIC   AND    ARGUMENT 

6.  What  are  the  legitimate  uses  of  the  argumcnta  ad 
jndicium,  ad  populum,  etc  ? 

7.  Explain  several  points  of  view  from  which  fallacious 
reasoning  can  be  considered. 


CHAPTER   XIII 

1.  Define  inductive  reasoning.     Distinguish  between 
Perfect  and  Imperfect  Induction. 

2.  How  do  you  distinguish  between  Deduction  and 
Induction  ? 

3.  What  is  the  difference  between  the  formal  process 
in  the  two  kinds  of  reasoning  ? 

4.  What  are  the  rules  for  inductive  reasoning  ? 


CHAPTER  XIV 

1.  Define  what  is  meant  by  proof  and  its  two  kinds. 

2.  What  is  the  difference  between  proof  and  infer- 
ence ? 

3.  What  is  the  difference  between  direct  and  indirect 
proof  ? 

4.  Name  and  define  the  various  processes  involved 
in  proof. 

5.  How  should  arguments  be  classified  in  logical  dis- 
course ? 

6.  What  is  meant  by  analytic   and   synthetic   argu- 
ments? 

7.  Explain  the  nature  of  Personal  Arguments. 

8.  What  should  be  the  arrangement  of  arguments  ? 

9.  Apply  argumentation  with  analysis  to  the  following 
themes,  choosing   according  to  conviction  or  conven- 
ience whether  it  shall  be  proof  or  disproof : 

The  benefits  of  the  Crusades.  The  execution  of 
Charles  the  First.  The  punishment  of  Socrates.  The 
policy  of  protection.  The  policy  of  free  trade.  The 


QUESTIONS    AND    EXAMPLES 


233 


merits  of  the  classics.  Co-education.  The  freedom  of 
the  press.  College  athletics.  The  benefits  or  evils  of 
feudalism.  The  character  of  Aaron  Burr.  The  ban- 
ishment of  Napoleon.  The  execution  of  the  Due 
d'Enghien.  The  Hispano-American  war.  Civil-service 
reform.  Universal  suffrage.  States  rights.  The  Pel- 
oponnesian  war.  Lynch  law.  Strikes.  Boycotting. 
The  necessity  of  labor  unions.  Free  education.  Trusts. 
Political  bosses. 

The  instructor  may  find  it  best  to  supply  subjects  of 
current  interest. 


PRACTICAL   EXERCISES 

DEDUCTIVE 

1.  Personal  deformity  is  an  affliction  of  nature. 
Disgrace  is  not  an  affliction  of  nature. 
Therefore  personal  deformity  is  not  a  disgrace. 

2.  None  but  animals  are  quadrupeds. 
Horses  are  quadrupeds. 
Therefore  horses  are  animals. 

3.  All  roses  are  beautiful. 
Lilies  are  not  roses. 
Therefore  lilies  are  not  beautiful. 

4.  Every  book  is  liable  to  error. 
Every  book  is  a  human  production. 

Therefore  all  human  productions  are  liable  to  error. 

5.  All  paper  is  useful  ;  and  as  all  that  is  useful  to  men 
is  a  source  of  comfort  to  them,  therefore,  all  paper  is  a 
source  of  comfort  to  them. 

6.  Some   statesmen  are  also  authors  ;    for  such  are 
Burke,  Macaulay,  Gladstone,  Lord  Russell,  etc. 

7.  Some  philosophers  are  logicians. 

No  logicians  are  ignorant  of  the  works  of  Aristotle. 
Therefore  some   philosophers  are  not  ignorant  of 
the  works  of  Aristotle. 


234  LOGIC   AND    ARGUMENT 

8.  No    persons    destitute    of   imagination    are    true 
poets. 

Some  persons  destitute  of  imagination  are  good 

logicians. 
Therefore  some  true  poets  are  not  good  logicians. 

9.  If  Caesar  was  a  tyrant  he  deserved  to  die. 
Caesar  was  not  a  tyrant. 

Therefore  he  did  not  deserve  to  die. 

10.  Good  is  the  object  of  moral  approbation.     The 
highest  good  is,  therefore,  the  ultimate  object  of  such 
approbation. 

11.  If  it  stops  raining  the  weather  will  be  colder. 
The  weather  will  be  colder. 

Therefore  it  will  stop  raining. 

12.  It  is  doubtful  whether  Caesar  will  come  forth  to- 
day or  not. 

For  he  is  superstitious  grown  of  late. 

13.  Every  man  should  be  moderate ;   for  excess  will 
Cause  disease. 

14.  All  Parisians  are  Frenchmen. 
No  Chinese  are  Parisians. 

Therefore  some  Chinese  are  not  Frenchmen. 

15.  Some  men  are  not  virtuous. 
All  Americans  are  men. 

Therefore  some  Americans  are  not  virtuous. 

16.  Blessed  are  the  merciful ;  for  they  shall  obtain 
mercy. 

17.  As  almost  all  the  organs  of  the  body  have  a  known 
use,  the  spleen  must  have  some  use. 

1 8.  Some  of  the  inhabitants  of  the  globe  are  more  civ- 
ilized than  others. 

No  savages  are  more  civilized  than  others. 
Therefore,  some  savages  are  not  inhabitants  of 
the  globe. 

19.  Cogito  ergo  sum  (I  think,  therefore,  I  am). 

20.  He  must  be  a  Mohammedan,  for  all  Mohamme- 
dans hold  these  opinions. 


QUESTIONS    AND    EXAMPLES  235 

21.  He  must  be  a  Christian,  for  only  Christians  hold 
these  opinions. 

22.  Logic  is  either  a  science  or  an  art. 
It  is  a  science. 

Therefore,  it  is  not  an  art. 

23.  No  idle  person  can  be  a  successful  writer  of  his- 
tory ;  therefore,  Hume,  Macaulay,  Hallam,  and  Grote 
must  have  been  industrious. 

24.  Every  moral  man  obeys  the  law  ;  every  citizen 
does  not  do  so,  and  therefore  is  not  moral. 

25.  This   explosion   must  have  been   occasioned   by 
gunpowder  ;  for  only  gunpowder  had  a  sufficient  force. 

26.  Rational  beings  are  accountable  for  their  conduct ; 
brutes  not  being  rational  are  exempt  from  responsibility. 

27.  All  valid  syllogisms  have  three  terms. 
This  syllogism  has  three  terms. 
Therefore,  this  syllogism  is  valid. 

28.  All  syllogisms  are  valid  that  have  three  terms. 
This  syllogism  has  three  terms. 
Therefore,  this  syllogism  is  valid. 

29.  Comets   are   heavy   matter  :    for  otherwise   they 
would  not  obey  gravitation. 

30.  A  charitable  man  has  no  merit  in  relieving  dis- 
tress, because  he  merely  does  what  is  pleasing  to  him- 
self. 

31.  If  the  government  enacts  such  a  law  it  must  either 
adopt  socialism  or  go  into  bankruptcy.     But  it  will  not 
enact  such  a  law,  and  hence  there  is  no  danger  of  either 
socialism  or  bankruptcy. 

32.  None  but  savages  were  in  America  when  it  was 
discovered. 

The  Hottentots  were  savages. 
Therefore,  they  were  in  America  when  it  was  dis- 
covered. 

33.  None  but  despots  possess  absolute  power. 
The  Czar  of  Russia  is  a  despot. 
Therefore,  he  possesses  absolute  power. 


236  LOGIC    AND    ARGUMENT 

34.  Bacon  was  a  great  philosopher  and    statesman, 
and  he  was  also  a  lawyer  ;  we  may  infer  that  any  lawyer 
may  be  a  great  philosopher  and  statesman. 

35.  Mathematical   studies   undoubtedly  improve   the 
reasoning  powers ;  but  as  logic  is  not  a  mathematical 
study  we  may  conclude  that  it  does  not  improve  our  rea- 
soning powers. 

36.  If  a  man  cannot  obey  the  law  he  must  be  either  a 
machine  or  a  demon  ;  but  no  man  is  either  of  these,  and 
hence  he  must  be  able  to  obey  the  law. 

37.  Whatever  tends  to  draw  the  mind  from  pursuits 
of  a  low  nature  deserves  to  be   promoted.     Classical 
learning  does  this,  since  it  gives  us  a  taste  for  intellectual 
enjoyments  :  therefore,  it  deserves  to  be  promoted. 

38.  If  virtue  is  involuntary,  vice  is  involuntary. 
Vice  is  voluntary. 

Therefore,  virtue  is  voluntary. 

39.  All  civilized  people  are  inhabitants  of  the  temper- 
ate zones.     Few  Indians  are  civilized,  and  therefore  few 
Indians  are  inhabitants  of  the  temperate  zones. 

40.  If  pain  is  severe  it  will  be  brief,  and  if  it  last  long 
it  will  be  slight ;  it  is  either  severe  or  it  lasts  long,  and 
therefore  will  be  either  brief  or  slight. 

41.  Some  who  are  truly  wise  are  not  learned  ;  but  the 
virtuous  alone  are  truly  wise ;  the  learned,  therefore, 
are  not  always  virtuous. 

FORMAL  AND   MATERIAL 

42.  The  Americans  are  a  nation,  and  as  the  citizens 
of  New  York  City  are  Americans,  they  must  be  a  nation. 

43.  The  right  should  be  enforced  by  law.     Hence, 
since  the  exercise  of  the  suffrage  is  a  right,  it  should  be 
enforced  by  law. 

44.  Napoleon  was  not  a  great  emperor  ;  for  though 
he  would  have  been  great  had  he  succeeded  in  retaining 
power,  he  did  not  do  so. 


QUESTIONS    AND    EXAMPLES  237 

45.  Seven  and  nine  are  odd  numbers. 
Sixteen  is  seven  and  nine. 
Therefore  sixteen  is  an  odd  number. 

46.  If  capital  punishment  involves  cruelty  to  its  vic- 
tims it  ought  to  be  abolished  in  favor  of  some  other  pen- 
alty ;   if  it  does  no  good  to  society  it  should  also  be 
abolished.     But  it  either  involves  cruelty  to  its  victims 
or  does  no  good  to  society,  and  hence  it  ought  to  be 
abolished. 

47.  The  Reformers  were  strongly  opposed  to  the  papal 
supremacy,  and  as  Mr.  B.  was  a  reformer,  because  he 
favored  better  politics,  he   was  opposed  to  the  papal 
supremacy. 

48.  Knowledge  is  of  no  use  to  anyone  in  preventing 
him  from  committing  crime  ;  for  we  hear  every  day  of 
frauds  and  forgeries  which  would  have  never  been  com- 
mitted had  not  the  person  learned  to  read  and  write. 

49.  Wealth  is  valuable  ;  value  is  purchasing  power ; 
purchasing  power  is  the  product  of  labor,  and  the  prod- 
uct of  labor  is  property  ;  therefore,  wealth  is  property. 

50.  Every  rule  has  exceptions  ;  this  is  a  rule,   and 
therefore  has  exceptions  ;  therefore,  there  are  some  rules 
that  have  no  exceptions. 

51.  All  who  think  this  man  innocent  think  he  should 
not  be  punished ;  you  think  he  should  not  be  punished  ; 
therefore,  you  think  him  innocent. 

52.  All  who  think  this  man  innocent  think  he  should 
not  be  punished  ;  you   think  he  should  be  punished ; 
therefore,  you  do  not  think  him  innocent. 

53.  The  end  of  punishment  is  either  the  protection  of 
society  or  the  reformation  of  the  criminal.     Capital  pun- 
ishment ought,   therefore,  to  be  abolished,   because  it 
neither  prevents  crimes  of  violence,  nor  protects  society, 
nor  does  it  reform  the  criminal. 

54.  Haste  makes  waste,  and  waste  makes  want.     A 
man,  therefore,  never  loses  by  delay. 

55.  Only  the  virtuous  are  truly  noble  ;  some  who  are 


238  LOGIC   AND    ARGUMENT 

called  noble  are  not  virtuous  ;  therefore,  some  who  are 
called  noble  are  not  truly  noble. 

56.  All    equilateral    triangles   are   equiangular,    and 
therefore,  all  equiangular  triangles  are  equilateral. 

57.  For  those  bent  on  cultivating  their  minds  by  dili- 
gent study  the  incitement  of  academic  honors  is  unnec- 
essary ;  and  it  is  ineffectual  for  the  idle  and  such  as  are 
indifferent  to  mental  improvement ;  therefore,  the  in- 
citement of  academic  honors  is  either  unnecessary  or 
ineffectual. 

58.  Logic,  as   it   was   cultivated   by   the   schoolmen, 
proved  a  fruitless  study ;  therefore,  logic  as  it  is  culti- 
vated to-day  must  be  a  fruitless  study. 

59.  A,  B,  C,  D,  and  E  are  the  only  German  students 
that  I  know  ;  they  are  all  men  of  considerable  intellect- 
ual attainments,  and  consequently  I  may  infer  that  all 
German  students  are  men  of  considerable  intellectual 
attainments. 

60.  Repentance  is  a  good  quality  ;  wicked  men  abound 
in  repentance,  and  therefore  abound  in  what  is  good. 

61.  Warm  countries  alone  produce  wine.     Spain  is  a 
warm  country,  and  therefore  produces  wine. 

62.  It  is  an  intensely  cold  climate  that  is  sufficient  to 
freeze  mercury ;  the  climate  of  Siberia  is  sufficient  to 
freeze  it,  and  hence  must  be  intensely  cold. 

63.  No  designing  person  ought  to  be  trusted  ;  engrav- 
ers are,  by  profession,  designing  persons  or  designers; 
therefore,  they  ought  not  to  be  trusted. 

64.  I  will  not  do  this  act  because  it  is  unjust ;   I  know 
it  is  unjust  because  my  conscience  tells  me  so,  and  my 
conscience  tells  me  so  because  the  act  is  wrong. 

65.  Is  a  stone  a  body  ?     Yes.     Then  is  not  an  animal 
a  body  ?    Yes.    Are  you  an  animal  ?     I  think  so.     Ergo, 
you  are  a  stone,  being  a  body. 

66.  If  ye  were  Abraham's  children  ye  would  do  the 
works  of  Abraham. — John  viii,  39. 

67.  He  that  is  of  God  heareth  God's  words  ;  ye  there- 


QUESTIONS   AND    EXAMPLES  239 

fore  hear  them  not,  because  ye  are  not  of  God.—JoAn 
viii,  47. 

68.  His  imbecility  of  character  might  have  been  in- 
ferred from  his  proneness  to  favorites  ;    for   all   weak 
princes  have  this  failing. 

69.  He  is  brave  who  conquers  his  passions  ;  he  who 
resists  temptation  conquers  his  passions  ;  so  that  he  who 
resists  temptation  is  brave. 

70.  Suicide  is  not  always  to  be  condemned  ;  for  it  is 
but  voluntary  death,  and  this  has  been  gladly  embraced 
by  many  of  the  greatest  heroes  of  antiquity. 

71.  All  that  glitters  is  not  gold;  tinsel  glitters  and 
therefore  is  not  gold. 

72.  Meat  and  drink  are  the  necessaries  of  life.     The 
revenues  of  the  king  were  spent  on  meat  and  drink,  and 
were  therefore  spent  on  the  necessaries  of  life. 

73.  Nothing  but  the  express-train  carries  the  mail, 
and  as  the  last  train  was  the  express,  it  must  have  car- 
ried the  mail. 

74.  Theft  is  a  crime  ;  theft  was  encouraged  by  the 
laws  of  Sparta  ;  therefore,  the  laws  of  Sparta  encour- 
aged crime. 

75.  Since  all  gold  is  a  metal,  the  most  rare  of  all 
masses    of   gold   must    be    the    most   rare  of  all   the 
metals. 

76.  He  who  calls  you  a  man  speaks  truly ;  he  who 
calls  you  a  fool  calls  you  a  man  ;  therefore,  he  who  calls 
you  a  fool  speaks  truly. 

77.  Protective  laws  should  be  abolished,  for  they  are 
injurious  if  they  produce  scarcity,  and  they  are  useless 
if  they  do  not. 

78.  Detention  of  property  implies  at  least  possession; 
for  detention  is  natural  possession. 

79.  Profit  is  interpreted  or  defined  to  be  advantage  ; 
to  take  profit  then  is  to  take  advantage.     It  is  wrong  to 
take  advantage  of  one's  neighbor,  and  therefore  it  is 
wrong  to  take  profit. 


240  LOGIC    AND    ARGUMENT 

80.  Peel's  remission  of  taxes  was  beneficial ;  the  taxes 
remitted  by  Peel  were  indirect,  and  therefore  the  re- 
mission of  indirect  taxes  is  beneficial. 

8r.  Some  poisons  are  vegetable  ;  not  poisons  are  use- 
ful drugs,  and  therefore  some  useful  drugs  are  not  vege- 
table. 

82.  Whosoever  intentionally  kills  another  should  suf- 
fer death ;    a  soldier,  therefore,  who   kills   his   enemy 
should  suffer  death. 

83.  Few  towns  in  the  country  have  500,000  inhabi- 
tants, and  since  all  such  towns  ought  to  have  three  repre- 
sentatives in  Congress,  it   is   evident   that   few   towns 
should  have  three  representatives. 

84.  If  Bacon's  opinion  be  right  it  is  improper  to  stock 
a  new  colony  with  criminals  from  prison  ;  but  this  course 
we  must  allow  to  be  proper  if  the  method  of  colonizing 
New  South  Wales  be  a  wise  one.     If  this  be  wise,  there- 
fore, Bacon's  opinion  is  not  right. 

85.  The  people  of  the  country  are  suffering  from  fam- 
ine, and  as  A,  B,  and  C   are  people  of  the  country, 
they  must  be  suffering  from  the  famine. 

86.  You  are  not  what  I  am  ;  I  am  a  man  ;  therefore, 
you  are  not  a  man. 

87.  Gold  and  silver  are  wealth  ;    and  therefore  the 
diminution  of  the  gold  and  silver  of  a  country  by  expor- 
tation is  a  diminution  of  the  wealth  of  the  country. 

88.  The  holder  of  some  shares  in  a  lottery  is  sure  to 
gain  a  prize,  and  as  I  am  the  holder  of  some  shares  in  a 
lottery  I  am  sure  to  gain  a  prize. 

89.  A  monopoly  of  the  sugar-refining  business  is  bene- 
ficial to  sugar  refiners ;  and  of  the  corn  trade  to  corn 
growers  ;  and  of  the  silk  manufacturers  to  the  silk  weav- 
ers ;  of  labor  to  the  laborers.     Now,  all  these  classes  of 
man  make  up  the  community.     Therefore,  a  system  of 
restriction   upon  competition  is  beneficial  to  the  com- 
munity. 

90.  Over-credulous  persons  should  never  be  believed, 


QUESTIONS   AND    EXAMPLES  241 

and  as  the  ancient  historians  were  in  many  instances 
over-credulous  they  ought  never  to  be  believed. 

91.  That  is  unfortunate  ;  you  insolently  assert  that  you 
are  a  Darwinian,  while  the  truth  is  that  you  are  a  poet. 

92.  Every  incident  in  the  narrative  is  probable,  and 
hence  the  narrative  may  be  believed,  since  it  is  probable. 

93.  If  a  substance  is  solid  it  possesses  elasticity,  and 
so  also  it  does  if  it  be  liquid  or  gaseous  ;  but  all  sub- 
stances are  either  solid,  liquid  or  gaseous  ;  therefore, 
all  substances  possess  elasticity. 

94.  Who  is  most  hungry  eats  most ;  who  eats  least  is 
most  hungry  ;  therefore,  who  eats  least  eats  most. 

95.  If  the  elixir  of  life  is  of  any  value  those  who  take 
it  will  improve  in  health  ;  now,  my  friend  who  has  been 
taking  it  has  improved  in  health,  and  therefore  the  elixir 
is  of  value. 

96.  What  produces    intoxication    should  be  prohib- 
ited ;   the   use   of  intoxicating  liquors   causes  intoxica- 
tion ;  therefore,  the  use  of  spirituous  liquors  should  be 
prohibited. 

97.  When  we  hear  that  all  the  righteous  people  are 
happy,  it  is  hard  to  avoid  exclaiming,  what  !  are  all  the 
unhappy  persons  we  see  thought  to  be  unrighteous  ? 

98.  Italy  is  a  Catholic  country,  and  abounds  in  beg- 
gars ;  France  is  also  a  Catholic  country,  and  therefore 
abounds  in  beggars. 

99.  If  it  be  fated  that  you  recover  from  your  present 
disease,  you  will  recover,  whether  you  call  in  a  doctor 
or  not ;  again,   if  it  be  fated  that  you  do  not  recover 
from  your  present  disease,  you  will  not  recover,  whether 
you  call  in  a  doctor  or  not.     But  one  or  the  other  of 
these  contradictories  is  fated,  and  therefore  it  can  be  of 
no  service  to  call  in  a  doctor. 

100.  All  the  trees  in  the  park  make  a  thick  shade  ; 
this  oak  tree  is  one  of  them,  and  therefore  makes  a  thick 
shade. 

101.  All  visible  bodies  shine  by  their  own  or  by  re- 

16 


242  LOGIC    AND    ARGUMENT 

fleeted  light.  The  moon  does  not  shine  by  its  own  ; 
therefore,  it  shines  by  reflected  light ;  but  the  sun  shines 
by  its  own  ;  therefore,  it  cannot  shine  by  reflected  light. 

102.  The  two  propositions,  "  Aristotle  is  Living,"  and 
"  Aristotle  is  Dead,"  are  both  intelligible  propositions  ; 
they  are  both  of  them  true  or  both  of  them  false,  because 
all  intelligible  propositions  must  be  either  true  or  false. 

103.  I  am  charged  with  absenteeism  from  my  post, 
and  on  that  ground  I  am  accused  of  ignorance  in  regard 
to  the  proper  duties  of  my  office.     But  my  accuser  him- 
self, who  was  my  predecessor  in  the  same  office,  was 
not  longer  than  five  days  in  the  country  of  which  he  was 
the  chief  officer. 

104.  Every  law  is  either  useless  or  it  occasions  hurt  to 
some  person ;   now,  a  law  that  is  useless  ought  to  be 
abolished  ;  and  so  ought  every  law  that  occasions  hurt ; 
therefore,  every  law  ought  to  be  abolished. 

105.  Does  a  grain  of  millet  when  dropped  on  the  floor 
make  a  sound?     No.     Does  a  bushel  of  millet  make  any 
sound  under  the  same  circumstances  ?     Yes.     Is  there 
not  a  determinate  proportion  between  the  bushel  and 
the  grain  ?     There  is.     There  must,  therefore,  be  the 
same  proportion  between  the  sonorousness  of  the  two. 
If  one  grain  be  not  sonorous,  neither  can  ten  thousand 
grains  be  so. 

106.  Injustice  is  more  profitable  than  justice,  because 
those  who  do  unjust  acts  gain  more  than  the  just. 

107.  Ruminant  animals  are  those  who   have  cloven 
feet,  and  they  usually  have  horns  ;  the  extinct  animal 
which  left  this  foot-print  had  a  cloven  foot ;  therefore,  it 
was  a  ruminant  animal  and  had  horns.     Again,  as  no 
beasts  of  prey  are  ruminant  animals,  it  cannot  have  been 
a  beast  of  prey. 

108.  Happiness  signifies  a  gratified  state  of  all  the 
faculties.     The  gratification  of  faculty  is  produced  by 
exercise.     To  be  agreeable  that  exercise  must  be  pro- 
portionate to  the  power  of  the  faculty ;  if  it  is  insuffi- 


QUESTIONS    AND    EXAMPLES 


243 


cient  discontent  arises,  and  its  excess  produces  weari- 
ness. Hence,  to  have  complete  felicity  is  to  have  all 
the  faculties  exerted  in  the  ratio  of  their  several  develop- 
ments. 

109.  I  am  offered  a  sum  of  money  to  assist  this  person 
in  gaining  the  office  he  desires ;  to  assist  a  person  is  to 
do  him  good,  and  no  rule  of  morality  forbids  the  doing 
of  good ;  therefore,  no  rule  of  morality  forbids  my  re- 
ceiving the  sum  of  money  for  assisting  this  person  to 
obtain  office. 

no.  We  must  either  gratify  our  vicious  propensities 
or  resist  them  ;  the  former  course  will  involve  us  in  sin 
and  misery  ;  the  latter  requires  self-denial.  Therefore, 
we  must  either  fall  into  sin  or  practise  self-denial. 

111.  He  that  can  swim  needs  not  despair  to  fly;  for 
to  swim  is  to  fly  in  a  grosser  fluid,  and  to  fly  is  to  swim 
in  a  subtler  fluid. 

112.  Every  moral  aim  requires  the  rational  means  of 
attaining  it ;  these  means  are  the  establishment  of  laws  ; 
and  as  happiness  is  the  moral  aim  of  man  it  follows  that 
the  attainment  of  it  requires  the  establishment  of  laws. 

113.  The  several  species  of  brutes  were  created  to 
prey  upon  each  other,  and   consequently   the    human 
species  was  created  to  prey  upon  them. 

114.  If  any  objection  can  be  urged  to  justify  a  change 
of  established  laws,  no  laws  could  be  reasonably  main- 
tained ;  but  some  laws  can  be  reasonably  maintained  ; 
therefore,  no  objection  that  can  be  urged  will  justify  a 
change  of  established  laws. 

115.  Riches  are  for  spending,  and  spending  for  honor 
and  good   actions.     Therefore,    extraordinary   expense 
must  be  limited  by  the  worth  of  the  occasion. 

116.  If  our  rulers  could  be  trusted  always  to  look  to 
the  best  interests  of  their  subjects,  monarchy  would  be 
the   best   form   of  government.      But   they  cannot  be 
trusted  ;  therefore,  monarchy  is  not  the  best  form  of 
government. 


244  LOGIC   AND    ARGUMENT 

117.  The  good  is  pleasure,  for  it  results  from  the  due 
performance    of  proper  functions  ;  but  the  good"  is  a 
state  of  consciousness  ;  therefore,  the  good  is  a  state  of 
consciousness  which  results  from  the  due  performance 
of  proper  functions. 

1 1 8.  He  who  bears  arms  at  the  command  of  the  mag- 
istrate does  what  is  lawful  for  a  Christian  ;  the  Swiss  in 
the  French  service  and  the  British  in  the  American  ser- 
vice bore  arms   at   the   command   of  the   magistrate  ; 
therefore,  they  did  what  is  lawful  for  a  Christian. 

119.  No  soldiers  should  be  brought  into  the  field  who 
are  not  well  qualified  to  perform  their  duty  ;  none  but 
veterans  are  well  qualified  to  perform  their  part ;  there- 
fore, none  but  veterans  should  be  brought  into  the  field. 

1 20.  Improbable   events  happen    almost  every  day, 
but  what  happens  almost  every  day  is  a  very  probable 
event ;  therefore,  improbable  events  are  very  probable 
events. 

121.  The  object  of  war  is  durable  peace;  therefore, 
soldiers  are  the  best  peace-makers. 

122.  Confidence  in  promises  is  essential  to  human  in- 
tercourse and  commerce  ;  for  without  it  the  greatest  part 
of  our  conduct  would  proceed  upon  chance.     But  there 
can  be  no  confidence    in    promises  if  man    were    not 
obliged  to  perform  them  ;  the  obligation,  therefore,  to 
perform  promises  is  essential  to  the  same  ends  and  in 
the  same  degree. 

123.  The  minimum  visibile   is    the   least   magnitude 
which  can  be  seen  ;  no  part  of  it  alone  is  visible,  and 
yet  all  the  parts  of  it  must  affect  the  mind  in  order  that  it 
may  be  visible  ;  therefore,  every  part  of  it  must  affect 
the  mind  without  being  visible. 

124.  He  who  believes  himself  to  be  always  in  the  right 
in  his  opinion  lays  claim  to  infallibility  ;  you  always  be- 
lieve yourself  to  be  in  the  right  in  your  opinion  ;   there- 
fore, you  lay  claim  to  infallibility. 

125.  If  the  light  is  not  refracted  near  the  surface  of 


QUESTIONS    AND    EXAMPLES 


245 


the  moon  there  cannot  be  any  twilight  there  ;  but  if  the 
moon  has  no  atmosphere,  light  is  not  refracted  near  its 
surface  ;  therefore,  if  the  moon  has  no  atmosphere  it 
cannot  have  any  twilight. 

126.  What  you  say  is  that  virtue  is  the  power  of  at- 
taining good?  Yes.  And  you  would  say  that  goods 
are  such  as  health  and  wealth,  and  the  possession  of  gold 
and  silver,  and  having  office  and  honor  in  the  state — 
these  are  what  you  call  goods  ?  Yes,  all  these.  Then, 
according  to  Meno,  who  is  the  hereditary  friend  of  the 
great  king,  virtue  is  the  power  of  getting  silver  and  gold. 


MISCELLANEOUS 

INDUCTIVE  AND   DEDUCTIVE 

127.  Geometry  contemplates  figures.      Figure  is  the 
termination  of  magnitude  ;  but  extension  in  the  abstract 
has  no  definite  determinate  magnitude  ;  whence  it  fol- 
lows clearly  that  it  can  have  no  figure,  and  consequently 
is  not  the  object  of  Geometry. 

128.  The  newly  discovered  painting  must  be  a  Ru- 
bens ;  for  the  conception,  the  drawing,  the  tone  and  tints 
are  precisely  those  seen  in  the  authentic  works  of  that 
master. 

129.  In  nine  counties,  in  which  the  population  is  from 
100  to  150  per  square  mile,  the  births  to  loo  marriages 
are  396  ;  in  sixteen  counties,  with  a  population  of  15010 
200  per  square  mile,  the  births  are  39010  100  marriages. 
Therefore,   the  number  of  births  per  marriage  is  in- 
versely related  to  the  density  of  population,  and  contra- 
dicts Malthus's  theory  of  population. 

130.  "  Cramming"   for    examination   is    detrimental 
rather  than  otherwise  ;  for  I  have  noticed  that,  no  matter 
what  the  subject  is,  I  invariably  write  a  poor  paper  when 
I  "  cram,"  and  a  good  one  when  I  do  not. 


246  LOGIC   AND    ARGUMENT 

131.  If  the  earth  were  of  equal  density  throughout  it 
would  be  about  2>£  times  as  dense  as  water;  but  it  is 
about  5X  times  as  dense;  therefore,  the  earth  must  be 
of  unequal  density. 

132.  The  great  famine  in  Ireland  began  in  1845,  and 
increased  until  it  reached  a  climax  in  1848.     During  this 
time  agrarian  crime  increased  very  rapidly    until,    in 
1848,  it  was  more  than  three  times  as  great  as  in  1845. 
After  this  it  decreased  with  the  return  of  better  crops, 
until,  in    1851,  it  was  only  fifty  per  cent,  more  than  it 
was  in  1845.     It  is  evident  from  this  that  a  close  relation 
of  cause  and  effect  exists  between  famine  and  agrarian 
crime. 

133.  "Now  that  which  does  not  make  a  man  worse, 
how  can  it  make  a  man's  life  worse  ?    But  neither  through 
ignorance,  nor  having  the  knowledge  but  not  the  power 
to  guard  against  or  correct  these  things,  is  it  possible 
that  the  nature  of  the  universe  has  overlooked  them  ; 
nor  is  it  possible  that  it  has  made  so  great  a  mistake, 
either  through  want  of  power  or  want  of  skill,  that  good 
and  evil  should  happen  indiscriminately  to  the  good  and 
the  bad.     But  death  certainly,  and  honor  and  dishonor, 
pain  and  pleasure — all  these  things  happen  equally  to 
good  men  and  bad,  being  things  which  make  us  neither 
nor  worse.     Therefore,  they  are  neither  good  nor  evil." 
— Marcus  Aurelius. 

134.  If  the  majority  of  those  who  use  public  houses 
are  prepared  to  close  them  legislation  is  unnecessary ; 
but  if  they  are  not  prepared  for  such  a  measure,  then  to 
force  it  on  them  by  outside  pressure  is  both  dangerous 
and  unjust. 

135.  On  May  27,  1875,  a  remarkable  shower  of  small 
pieces   of  hay  occurred    at   Monkstown,   near  Dublin. 
They  appeared  floating  down  from  a  great  height.     A 
similar  shower  occurred  a  few  days  earlier  in  Denbigh- 
shire.    From  this  and  many  similar  facts  we  conclude 
that  the  distribution  of  organisms  over  continents  and 


QUESTIONS    AND    EXAMPLES  247 

islands  separated  by  the  ocean  has  been  effected  by  the 
agency  of  natural  forces. 

136.  The  influence  of  heat  in  changing  the  level  of  the 
ground  upon  which  the  Temple  of  Jupiter  Serapis  stands 
might  be  inferred  from  several  circumstances.     In  the 
first  place,  there  are  numerous  hot  springs  in  the  vicinity, 
and  when  we  reflect  on  the  dates  of  the  principal  oscilla- 
tions of  level  this  conclusion  is  made  much  more  prob- 
able.    Thus,  before  the  Christian  era,  when  Vesuvius 
was  regarded  as  a  spent  volcano,  the  ground  upon  which 
the  temple  stood  was  several  feet  above  water.     But 
after  the  eruption  of  Vesuvius  in  79  B.C.  the  temple  was 
sinking.     Subsequently,  Vesuvius  became  dormant,  and 
the   foundations  of  the    temple   began   rising.    Again 
Vesuvius    became   active    and    has   remained  so  ever 
since.     During  this  time  the  temple  has  been  subsiding 
again,  so  far  as  we  know  its  history. 

137.  This  person  may  reasonably  be  supposed  to  have 
committed  the  theft,    for  he  can  give  no  satisfactory 
account  of  himself  on  the  night  of  the  alleged  offence ; 
moreover,  he  is  a  person  of  bad  character,  and  being 
poor  is  liable  to  a  temptation  to  steal. 

138.  Don't  you  think  the  possession  of  gold  is  good  ? 
Yes,  said  Ctesippus,  and  the  more  the  better,  and  to 
have  money  everywhere  and  always  is  a  good.     Cer- 
tainly, a  great  good,  he  said.     And  you  admit  that  gold 
is  a  good  ?     I  have  admitted  that,  he   replied.     And 
ought  not  a  man  have  gold  everywhere  and  always,  and 
as  much  as  possible  in  himself,  and  may  not  he   be 
deemed  the  happiest  of  men  who  has  three  talents  of 
gold  in  his  stomach,  and  a  talent  in  his  head,  and  a 
stater  of  gold  in  his  eye. — Plato's  Dialogues. 

139.  It  has  been  found  that  linnets  when  shut  up  and 
educated  with  singing  larks— the  skylark,  woodlark,  or 
titlark— will  adhere  entirely  to  the  songs  of  these  larks 
instead  of  the  natural  song  of  the  linnets.     We  may  in- 
fer, therefore,  that  birds  learn  to  sing  by  imitation,  and 


248  LOGIC    AND    ARGUMENT 

that  their  songs  are  no  more  innate  than  language  is  in 
man. 

140.  The  policy  of  protection   was  immediately  fol- 
lowed by  a  great  increase  in  prosperity  and  wealth  of 
the  country,  and  hence  we  may  infer  that  the  result  was 
due  to  its  connection  with  the  enactment  of  the  protec- 
tive law.     In  reply,  however,  we  are  told  that  before  the 
passage  of  the  law  the  loss  by  fire  in  Chicago  in  one  year 
was  $200,000,000,  but  was  only  $3,000,000  for  the  year 
after  its  passage,  so  great  was  the  effect  of  this  act. 

141.  A  man  that  hath  no  virtue  in  himself  envieth 
virtue  in  others  ;  for  men's  minds  will  either  feed  upon 
their  own  good  or  upon  others'  evil,  and  who  wanteth  the 
one  will  prey  upon  the  other. 

142.  Five  years  ago  a  first-class  pair  of  nickel-plated 
steel  skates,  with  the  necessary  clamps  to  fasten  them  to 
the  boot  or  shoe,  cost  $15.     To  day,  precisely  the  same 
article,  and  with  an  equal  finish  and  completeness,  can 
be  obtained  for  $4.     Three  years  ago  a  second  grade 
of  nickel-plated  steel  skates  cost  $4.     The  same  article 
can  be  produced  to-day  for  $1.50.       The   decline   of 
seventy  per  cent,  in  five  years,  and  of  sixty  per  cent,  in 
three  years  shows  just  how  protection  cheapens  prices. 

143.  "'By  open  discrimination,  or  by  secret  rates, 
drawbacks,  and  rebates,  a  few  railway  managers  may 
subject  to  their  will  every  business  in  which  transporta- 
tion is  a  large  element  of  cost,  as  absolutely  as  any  ori- 
ental despot  ever  controlled  the  property  of  his  subjects. 
No  civilized  community  has  ever  known  any  body  of 
rulers  with  such  power  to  distribute  at  pleasure,  among 
its  mercantile  classes,  prosperity  or  adversity,  wealth 
or  ruin.      That  this  is  no  abstract  or  remote  danger  to 
society  is  plain  to  any  man  who  will  look  at  the  condi- 
tion of  trade  and  of  mercantile  morals  in  the  United 
States  to-day.'     How  vivid  !     But  how  absurd  !  how  un- 
true !     Our  commercial  morals  are  equal  to  the  highest 
in  the  world." 


QUESTIONS    AND    EXAMPLES  249 

144.  We  observe  very  frequently  that  very  poor  hand- 
writing characterizes  the  manuscripts  of  able  men,  while 
the  best  handwriting  is  as  frequent  with  those  who  do 
little  mental  work  when  compared  with  those  whose  pen- 
manship is  poor.     We  may  infer,  therefore,  that  poor 
penmanship  is  caused  by  the  influence  of  severe  mental 
occupation. 

145.  Since  there  is  no  harm  or  evil  to  the  elements 
themselves  in  their  continual  changes  into  one  another, 
a  man  should  have  no'apprehension  about  the  dissolution 
of  all  elements.      For  it  is  according  to  nature,  and 
nothing  is  evil   that  is  according  to  nature.— Marcus 
Aurelius. 

146.  "  Mr.  Gladstone,  however,  commits  himself  to 
the  principle  that  '  all  protection  is  bad.'     If  this  has 
been  his  belief  ever  since  he  became  an  advocate  of  free 
trade,  his  conscience  must  have   received   many   and 
severe  wounds,  as  session  after  session,  while  Chancellor 
of  the   Exchequer,   he   carried   through   Parliament   a 
bounty — may  I  not  say  a  direct  protection  ?— of  ^180,000 
to  a  line  of  steamers  running  between  England  and  the 
United  States — a  protection  that  began  six  years  before 
free  trade  was  proclaimed,  and  was  continued  nearly 
twenty  years  after." 


UC  SOUTHERN 


A'-  '•••null  HI   in   1 1| 
000  085  248 


